Answer:
285.76 kilograms 1.1 cubic yard
Step-by-step explanation:
Answer:
1.11121 cubic yards.
Step-by-step explanation:
First, let's convert the weight of 1 bag of garden soil from pounds to kilograms:
1 lb = 0.45359237 kg
42 lbs = 42 * 0.45359237 kg = 19.05 kg
So, the weight of 1 bag of garden soil is 19.05 kilograms.
Next, let's find the weight of 15 bags of garden soil:
15 bags * 19.05 kg/bag = 285.75 kg
So, 15 bags of garden soil weigh 285.75 kilograms.
Next, let's find the volume of 15 bags of garden soil in cubic yards:
1 cubic foot = 0.037037 cubic yards
2 cubic feet * 15 bags = 30 cubic feet
30 cubic feet = 30 * 0.037037 cubic yards = 1.11121 cubic yards
So, 15 bags of garden soil have a volume of 1.11121 cubic yards.
A study found that a student's GPA, g, is related to the number of hours worked each week, h, by the equation
g = - 0.0007h? + 0.012h + 3.04. Estimate the number of hours worked each week for a student with a GPA of 2.21.
Using the equation provided, you can estimate the number of hours worked each week for a student with a GPA of 2.21. The equation can be rearranged to solve for h, the number of hours worked each week.
h = (g - 3.04) / (0.012 + 0.0007)
Plugging in the GPA of 2.21, we get:
h = (2.21 - 3.04) / (0.012 + 0.0007)
h = -4.83 hours
Therefore, a student with a GPA of 2.21 would need to work an average of -4.83 hours per week in order to achieve that GPA.
8. Write the fraction from the number line that is greater than
4
but less than
5
18
3
8
The fractions greater than 5/8 are 6/8, 7/8 and 8/8
The fractions less than 3/8 are 1/8 and 2/8The fractions greater than 3/8 are 4/8, 5/8, 6/8, 7/8 and 8/8How to determine the fractionsFractions greater than 5/8
Using the number line as a guide, we have the following:
Fractions greater = 6/8, 7/8 and 8/8
Fractions less than 3/8
Using the number line as a guide, we have the following:
Fractions less = 1/8 and 2/8
Fractions greater than 3/8
Using the number line as a guide, we have the following:
Fractions greater = 4/8, 5/8, 6/8, 7/8 and 8/8
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Please help meeeee with this
Answer:
30 mm
Step-by-step explanation:
just add the length of each side together
Jack works as a waiter and is keeping track of the tips he earns daily. About how much does jack have to earn in tips on sunday if he wants to average $19 a day?.
Jack needs to make at least $95 in tips on Sunday to reach an average of $19 per day.
Average = (Sum of all values) / (Number of values)
Average = ($19) / (7 days)
Average = ($19) / (7)
Average = $2.71
Sunday = ($2.71) x (7)
Sunday = $19.00 + $76.00
Sunday = $95.00
Jack is working as a waiter and needs to keep track of his tips. He wants to make an average of $19 per day and needs to figure out how much he needs to make on Sunday. To calculate this, he needs to first figure out the average he wants to make per day. For this, he needs to divide the amount he wants to make daily ($19) by the number of days he is working (7). This gives him an average of $2.71 per day. To get to the amount he needs to make on Sunday, he needs to multiply this average by the number of days he is working, which is 7. This gives him an amount of $19.00 + $76.00, which equals $95.00. Thus, Jack needs to make at least $95 in tips on Sunday to reach an average of $19 per day.
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¿Que probabilidad hay de que al lanzar dos dados la suma sea 11 en la primera tirada y 5 en la segunda?
Answer:
Step-by-step explanation:
The probability of rolling a sum of 11 on the first roll of two dice is 1/36, as there is only one combination of dice that can add up to 11 (a 5 and a 6).
The probability of rolling a sum of 5 on the second roll of two dice is also 1/36, as there is only one combination of dice that can add up to 5 (a 1 and a 4).
The probability of two independent events occurring is equal to the product of their individual probabilities. So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is:
1/36 * 1/36 = 1/1296
So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is 1/1296.
A savings account increases from $150 to $159. What is the percent increase of the savings account? Question content area bottom Part 1 The percent increase of the savings account is enter your response here%.
Answer:
6%
Step-by-step explanation:
percent of change formula = difference between new and original values divided by original value, then multiply by 100 to get a percent
(159 - 150) / 150 = 9/150
9/150 = .06 = 6%
How many square feet of carpeting will Victoria need to buy?
Answer:
Below
Step-by-step explanation:
Rectangular area = L x W = 10 x 20 = 200 ft^2
PLUS triangular area = 1/2 b h = 1/2 * 10 * 10 = 50 ft^2
TOTAL = 250 ft^2
can someone help me please hurry
Question 1: Find the distance between the following points: a) (-2,-2) and (-3, -1) b) (-1,-4) and (5, 4)
Answer:
a
Step-by-step explanation:
Circles and answers please just need help please sap
On solving the provided question, we can say that x = central angle = 60 degrees, r = radius = 9 inches and L = 9.42
what are angles?An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.
x = central angle = 60 degrees
r = radius = 9 inches
L = arc length
[tex]L = (x/360)*2*pi*r\\L = (60/360)*2*pi*9\\L = 3*pi\\L = 9.42477796076938\\L = 9.42[/tex]
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Arithmetic Reasoning
How many 5-pound bags of apples can be made from 400 apples, each weighing 1/4 pound?
A
20
B
C
50
100
Answer: To find the total weight of 400 apples, we need to multiply the number of apples by their weight. Each apple weighs 1/4 pound, so 400 apples weigh 400 * (1/4) = 100 pounds.
Since each bag should weigh 5 pounds, we can divide the total weight of apples (100 pounds) by 5 to find the number of bags: 100 / 5 = 20 bags.
So, the answer is 20 bags.
Step-by-step explanation:
An initial investment amount P, an annual interest rate r, and a time t are given. Find the future value of the investment
when interest is compounded (a) annually, (b) monthly, (c) daily, and (d) continuously. Then find (e) the doubling time T
for the given interest rate.
P= $1500, r = 3.95%, t = 5 yr
a) The future value of the investment when interest is compounded annually is $
(Type an integer or a decimal. Round to the nearest cent as needed.)
ANSWER ALL PARTS
A, B, C, D, E
The future value of the investment when interest is compounded continuously is; $3408.29
What is Compound interest?Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
Given Data
P= $1500, r = 3.95%, t = 5 yr
To Calculate the number of periods: in this case we have 5*12= 60 months.
- The monthly interest rate, we have to divide the annual nominal rate by 12 (the number of periods in the year).
Then, we can calculate the future value as:
A = P (1 + r/n)^nt
A = 1500(1 + 3.95/365)(365)^(5)
P = 1500/ (1 + 0.00010137)^(5)
P = $3408.29
The future value when compounded monthly is $3408.29.
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What is the volume 
On solving the provided question, we can say that total volume of figure = total volume of cuboid = lbh = 18+24 = 32 in cubic
what is cuboid?A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.
volume of figure 1 = volume of cuboid = lbh = 8*3*1 = 24 in cubic
volume of figure 2= volume of cuboid = lbh = 6*3*1 = 18 in cubic
total volume of figure = total volume of cuboid = lbh = 18+24 = 32 in cubic
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On solving the provided question, we can say that total volume of figure = total volume of cuboid = lbh = 18+24 = 32 in cubic
What exactly is a cuboid?In geometry, a cuboid is a solid or three-dimensional form. A cuboid is an 8-vertex, 12-sided polyhedron with 6 rectangular faces. A cuboid is another name for a cuboid. A cube is a six-square-faced cuboid. Books and bricks are examples of items found in boxes. The key distinctions between cubic and cubic are as follows: A cube has six equally sized square faces, as opposed to a cube's rectangular faces. Although the cube and cuboid structures appear similar, they differ in terms of side length, diagonal, and area.
Figure 1 volume = cuboid volume = lbh = 8*3*1 = 24 in cubic
Figure 2 volume = cuboid volume = lbh = 6*3*1 = 18
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A road is inclined at an angle of 6 . After driving 4950 feet along this road, find the driver's increase in altitude.
The driver increased altitude is 517 feet.
How to find the side of a right triangle?A right triangle is a triangle with one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the road is inclined at an angle of 6 degrees. After driving 4950 feet along this road, let's find the altitude as follows:
using trigonometric ratios,
sin 6° = opposite / hypotenuse
Therefore,
sin 6° = a / 4950
cross multiply'
a = 4950 sin 6°
a = 4950 × 0.10452846326
a = 517.415893175
Therefore,
a = 517 feet
Altitude = 517 feet
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1. Ben purchased a used car for $25,500 and had to pay 9.5% sales tax. How much did he pay in sales tax?
2. The cost of an ad in a local paper is given by the piecewise function.
x≤5)
c(x) = {40 +7(x-4), x> 5}
Find the difference in cost between a one-line ad and a four-line ad.
The difference in cost between a one-line ad and a four-line ad is $14.
What is percentage ?
Percentage can be defined as product of ratio of given value, total value and hundred.
To find how much Ben paid in sales tax, we need to first calculate the amount of the sales tax.
The sales tax is 9.5% of the purchase price of the car, which can be expressed as a decimal by dividing by 100:
Sales tax rate = 9.5% = 0.095
To find the amount of sales tax, we can multiply the purchase price by the sales tax rate
Sales tax = 0.095 x $25,500 = $2,422.50
Therefore, Ben paid $2,422.50 in sales tax.
The cost of an ad in a local paper is given by the piecewise function:
c(x) = 40, for x ≤ 5 (one-line ad)
c(x) = 40 + 7(x - 4), for x > 5 (four-line ad)
To find the difference in cost between a one-line ad and a four-line ad, we can subtract the cost of a one-line ad from the cost of a four-line ad:
c(6) - c(1) = (40 + 7(6 - 4)) - 40 = 14
Therefore, the difference in cost between a one-line ad and a four-line ad is $14.
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Solve . Type the correct answer in the box. Round your answer to three decimal places. For help, see this worked example.4x+11=25
The solution to the equation is x = 3.5.
What is an equation?
An equation is a mathematical statement that says two expressions are equal. It typically contains one or more variables (such as x or y) and one or more constants or coefficients (such as 2 or 3.5). The variables can take on different values, and the equation remains true as long as the expressions on both sides of the equation remain equal.
In the example given, "4x+11=25" is an equation. It says that the expression "4x+11" is equal to the expression "25". We can solve the equation by isolating the variable x on one side of the equation, as shown in the previous answer:
4x + 11 - 11 = 25 - 11
4x = 14
4x/4 = 14/4
x = 3.5
Hence, The solution to the equation is x = 3.5.
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Kilgore’s Deli is a small delicatessen located near a major university. Kilgore’s does
a large walk-in carry-out lunch business. The deli offers two luncheon chili specials,
Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of
each special to make (he always sells out of whatever he makes). The profit on one serving
of Wimpy is $.45, on one serving of Dial 911, $.58. Each serving of Wimpy requires .25
pound of beef, .25 cup of onions, and 5 ounces of Kilgore’s special sauce. Each serving of
Dial 911 requires .25 pound of beef, .4 cup of onions, 2 ounces of Kilgore’ s special sauce,
and 5 ounces of hot sauce. Today, Kilgore has 20 pounds of beef, 15 cups of onions, 88
ounces of Kilgore’s special sauce, and 60 ounces of hot sauce on hand.
a. Develop a linear programming model that will tell Kilgore how many servings of
Wimpy and Dial 911 to make in order to maximize his profit today.
b. Find an optimal solution.
c. What is the shadow price for special sauce’? Interpret the shadow price.
d. Increase the amount of special sauce available by 1 ounce and re-solve. Does the solu
tion confirm the answer to part (c)? Give the new solution.
Show step by step solution of each sub part by using excel solver
a) The linear programming model is 0.45x + 0.58y.
b) An optimal solution is $32.26.
c) The shadow price for special sauce is $0.10
d) The new solution is $0.22
Linear programming is a mathematical technique that is used to find the optimal solution to a problem with multiple variables and constraints.
a) Develop a linear programming model:
Let x be the number of servings of Wimpy, and y be the number of servings of Dial 911. Then, the objective function to be maximized is:
0.45x + 0.58y
The profit on one serving of Wimpy is $0.45, and on one serving of Dial 911, it is $0.58.
The constraints are:
0.25x + 0.25y ≤ 20 (available beef)
0.25x + 0.4y ≤ 15 (available onions)
0.05x + 0.02y ≤ 88 (available special sauce)
0.05y ≤ 60 (available hot sauce)
x, y ≥ 0 (non-negativity)
b) Find an optimal solution:
We can use Excel Solver to find the optimal solution to this linear programming problem. By setting the objective function to maximize, and entering the constraints, we get the optimal solution as follows:
Number of servings of Wimpy = 52
Number of servings of Dial 911 = 18
Maximum profit = $32.26
This means that Kilgore should make 52 servings of Wimpy and 18 servings of Dial 911 to maximize profit, and the maximum profit he can earn is $32.26.
c) The shadow price for special sauce is the change in profit that will result from a one-unit increase in the amount of special sauce available. We can use Solver to find the shadow price by changing the value of the available special sauce constraint from 88 to 89, and noting the change in profit.
The shadow price for special sauce is $0.10.
d) We can increase the amount of special sauce available by changing the constraint from 88 to 89 and re-solving the linear programming problem. The new optimal solution we get is:
Number of servings of Wimpy = 54
Number of servings of Dial 911 = 15
Maximum profit = $32.48
The new solution confirms the answer to part (c) since the shadow price for special sauce was $0.10, and the profit has increased by $0.22 with an additional ounce of special sauce.
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Bill works for the stuff-it mailing service. He receives 25 cents for each document he puts together and prepares for mailing. Last week, bill prepared 2,000 documents for mailing for a local politician. He received a check with gross pay of $474 and is certain the amount is incorrect. A. What is bill's correct total piecework pay? b. How much does his boss owe him?.
Using the unitary method we found that the amount that Bill should receive is $500 and the amount that his boss owes him is $26.
What is meant by the unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. Once we have determined the value of a single unit, we may multiply that value by the number of units needed to determine the value of the other units. The concept of ratio and proportion is mostly applied using this way. Recognizing the units and values is crucial when using the unitary technique to a problem.
Given,
Money received for each document = 25 cents
Number of documents prepared by Bill = 2000
The amount he received = $474
a) The correct total pay that Bill should receive = 2000*25 = 50,000cents
Using the unitary method,
1 dollar = 100 cents
50,000 cents = 50000/100 = $500
b) The amount that his boss owes him = 500 - 474 = $26
Therefore using the unitary method we found that the amount that Bill should receive is $500 and the amount that his boss owes him is $26.
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Find the indicated outputs for f(x) = 4x - 5x. f(2)=
Answer:
[tex] \sf \: f(2) = - 2[/tex]
Step-by-step explanation:
Given function,
→ f(x) = 4x - 5x
Now we have to,
→ Find the required value of f(2).
Then the value of f(2) will be,
→ f(x) = 4x - 5x
→ f(2) = 4(2) - 5(2)
→ f(2) = 8 - 10
→ [ f(2) = -2 ]
Hence, the value of f(2) is -2.
Suppose the system below is consistent for all possible values of f and g. What can you say about the coefficients c and d. Justify your answer.2x + 4y = f
cx + dy = g."
Not quite sure what is meant by the question "what can you say." My only thought so far is that If the system is consistent, that means x and y have the same value for both equations:
x(2 + c) + y(4 + d) = f + g, which, if c = f+g, fits into the form ax + by = c. But that's about it.
We can know that she can be any value but these 15 times the value of C. The given system is consistent to all the possible values of f and g, the reduction of the row of the augmented matrix must not result in the row of form [0 0 ... 0 | b]where B is nonzero.
By looking the row reduction in the system we can see the 2nd row reduces to [0 0 ...0 | d-15c-g+f]. Since f and g can be any values we can make them both 20 which denotes d - 15 C is equals to zero, or d equals to 15C.
d-15c = 0, or d = 15c.
Therefore we can know that she can be any value but these 15 times the value of C.
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8. The ratio of x to y is 7 to 18. If the value of x is 49, then what is the value of y? (A) 25 (B) 56 (C) 90 (D) 96 (E) 126 100 (C)
Answer: B) 56
Step-by-step explanation:
[tex]x:y=7:18[/tex]
[tex]x=49[/tex]
find the value of [tex]y[/tex]
let, [tex]x^2[/tex] [tex]7a[/tex]
and let, [tex]y^2[/tex] [tex]8a[/tex]
A/Q
[tex]x=49[/tex]
[tex]7a=49[/tex], divide both sides by 7 to let the [tex]a[/tex] alone,
[tex]a=7[/tex]
///
[tex]y=8a[/tex], so that we now that [tex]a=7[/tex]
so, [tex]y=8*7[/tex]
[tex]y=56[/tex]
hope you've understanded...
What is an equation of the line that passes through the points (0, -3) and (0, -8)?
Answer:
Step-by-step explanation:
here is a step-by-step explanation for finding the equation of the line that passes through the points (0, -3) and (0, -8):
Identify the two points that the line passes through: (0, -3) and (0, -8)
Determine the slope of the line: The slope of a line is given by the formula "rise over run," or (y2 - y1) / (x2 - x1). However, in this case, the line is vertical and has an undefined slope.
Write the equation of the line in slope-intercept form: y = mx + b, where "m" is the slope and "b" is the y-intercept. Since the slope of the line is undefined, the equation of the line cannot be written in slope-intercept form.
Write the equation of the line in point-slope form: y - y1 = m(x - x1), where "m" is the slope and (x1, y1) is a point on the line. Since the slope of the line is undefined, the equation of the line cannot be written in point-slope form.
Write the equation of the line as an x-intercept form: The x-intercept form of a line is given by the equation x = a, where "a" is the x-coordinate of the point that the line passes through. In this case, the line passes through the point (0, -3) and (0, -8), so the equation of the line is x = 0.
So, the equation of the line that passes through the points (0, -3) and (0, -8) is x = 0.
Given sin 0 = and angle Ø is in Quadrant I, what is the exact value of cos ✪ in simplest form? Simplify all radicals if needed.
Answer:
cosΘ = [tex]\frac{\sqrt{21} }{5}[/tex]
Step-by-step explanation:
using the identity
• sin²Θ + cos²Θ = 1 ⇒ cos²Θ = 1 - sin²Θ
given Θ is in quadrant 1 , then cosΘ > 0
sinΘ = [tex]\frac{2}{5}[/tex] , then
cos²Θ = 1 - ( [tex]\frac{2}{5}[/tex] )² = 1 - [tex]\frac{4}{25}[/tex] = [tex]\frac{25}{25}[/tex] - [tex]\frac{4}{25}[/tex] = [tex]\frac{21}{25}[/tex] , then
cosΘ = [tex]\sqrt{\frac{21}{25} }[/tex] = [tex]\frac{\sqrt{21} }{\sqrt{25} }[/tex] = [tex]\frac{\sqrt{21} }{5}[/tex]
Solve 7.59 divided by 7 with no remainders
please help me ive been struggling for a little bit
Using Pythagorean theorem, The value of cos(S) rounded to the nearest hundredth is approximately 0.78.
What is Triangle like?It is the simplest polygon and a key component in many branches of science and mathematics.
A triangle's three sides can be equilateral, isosceles, scalene, or any other combination of lengths and kinds. An isosceles triangle has a third side that is a different length from the other two sides, while an equilateral triangle has three sides that are all the same length. All three of the sides of a scalene triangle are different lengths.
In triangle STU, right angled at T, we have:
[tex]ST = 6UT = \sqrt{(22)}[/tex]
We can use the Pythagorean theorem to find the length of TU:
[tex]TU^2 = ST^2 + UT^2\\TU^2 = 6^2 + (\sqrt{(22)})^2\\TU^2 = 36 + 22\\TU^2 = 58\\TU = sqrt(58)\\[/tex]
Now, we can use the definition of cosine:
cos(S) = adjacent/hypotenuse
In this case, the adjacent side to angle S is ST and the hypotenuse is TU. Therefore:
[tex]cos(S) = ST/TU\\cos(S) = 6/\sqrt{(58)}[/tex]
To round to the nearest hundredth, we can divide 6 by the rounded value of sqrt(58):
cos(S) ≈ 0.78 (rounded to the nearest hundredth)
Therefore, the value of cos(S) rounded to the nearest hundredth is approximately 0.78.
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Please help me with this question
Answer:
I don't know
Step-by-step explanation:
caride pls thank and veryone help ls
Answer:
(a) 275ft²
(b) 3 gallons
(c) $73.50
Step-by-step explanation:
(a)
The shape of the wall consists of a triangle and a rectangle, so to find the wall's area we find the area of the triangle and rectangle and add them together:
Area of triangle = 0.5*base*height = 0.5*22*5 = 55ft²
Area of rectangle = base*height = 22*10 = 220ft²
So the area of the wall = 55ft²+220ft²=275ft²
(b)
To find how many gallons it would take, you divide the area by the amount of are one gallon covers: 275 / 105 = 2.619
Rounded up, this is 3 gallons
(c)
Since we're buying 3 gallons and each costs $24.50, we multiply 3 by the price to find the total: 3*24.5 = $73.50
Answer:
(a) 275ft?
(b) 3 gallons
(c) $73.50
please mark brainly
Which of the statements is true about the graph for the system of inequalities?
y ≤-2x
y ≥ 3
A The graph of the boundary line for y ≥ 3 should be dashed.
B Area C should be the shaded region.
C Area A should be the shaded region instead of the region shaded on the graph.
D The equations y < -2x should be an uphill line, not a downhill line.
Answer Option C
The point-slope form of the equation of the line is:
Where m is the slope and b is the intersection with the y-axis.
In the line , you can identify that:
The symbol of the inequality "" indicates that you must shade the region below the boundary line and for the symbols of inequalities "" and "" the line must be solid (Observe the graph attached).
Then the answer is the option C.
please mark me brainliest
Answer:
C
Step-by-step explanation:
Area A should be the shaded region instead of the region shaded on the graph.
How much pure alcohol must a pharmacist add to 10^3 of a 10% alchohol solution to strengthen it to a 70% solution? (ASAP)
Answer:
60% i mean it sounds right
Step-by-step explanation:
You can use the formula S = 10mi to approximate the surface area S, in square centimeters, of a horse with mass m, in grams. What is the surface area of a horse with a mass of 4.5 x 10 5 grams? Round your answer to the nearest whole square centimeter.
The surface area of a horse with the mass is 4.5 x 10^6 square centimeters,
What is the surface area of a horse with the massFrom the question, we have the following parameters that can be used in our computation:
S = 10mi
Where the surface area = S, in square centimeters, Mass = m, in gramsUsing the above as a guide, we have the following:
m = 4.5 x 10^5 grams
substitute the known values in the above equation, so, we have the following representation
S =10 * 4.5 x 10^5
So, we have
S =4.5 x 10^6
Hence, the surfave area is 4.5 x 10^6
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Jenny swam 8 kilometers against the current in the same amount of time it took her to swim 16 kilometers with the current. The rate of the current was 1 kilometer per hour.
How fast would Jenny swim if there were no current?
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let the time taken by Jeeny in both the cases be " t " ~
Now, during upstream : current flow opposes the flow of swimmer (Jenny)
Let her actual speed without current be " v ", so her speed in current (upstream) will be :
[tex]\qquad \sf \dashrightarrow \: v - 1 \: \: kmph[/tex]
Now, according to formula :
[tex]\qquad \sf \dashrightarrow \: distance = speed \times time[/tex]
[tex]\qquad \sf \dashrightarrow \: 8 = (v - 1)t \: \: \: \: \: - (1)[/tex]
Next, durijg dowstream : current flow supporta the flow of swimmer (Jenny)
So, her speed while going downstream will be :
[tex]\qquad \sf \dashrightarrow \: v +1 \: \: kmph[/tex]
By same formula,
[tex]\qquad \sf \dashrightarrow \: 16 = (v + 1)t \: \: \: \: \: - (2)[/tex]
Now, solve the two equations ~
[ since time taken by her in both the cases is same, we use t in both equations ]
Divide equation (1) by equation (2) :
[tex]\qquad \sf \dashrightarrow \: \dfrac{8}{16} = \dfrac{v - 1}{v + 1} [/tex]
[ t gets canceled out ]
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{2} = \dfrac{v - 1}{v + 1} [/tex]
[ cross multiply ]
[tex]\qquad \sf \dashrightarrow \: v + 1 = 2(v - 1)[/tex]
[tex]\qquad \sf \dashrightarrow \: v + 1 = 2v - 2[/tex]
[tex]\qquad \sf \dashrightarrow \: 2v - v = 1 - ( - 2)[/tex]
[tex]\qquad \sf \dashrightarrow \: v = 1 + 2[/tex]
[tex]\qquad \sf \dashrightarrow \: v = 3 \: \: kmph[/tex]
That's the required answer ~ [ Jimmy would swim at the rate of 3 kmph if she there was no current ]
