A summer biathalon-style race requires running a certain distance, and then biking a distance 2 miles more than the length of the run. One athlete has a running speed of 6 miles per hour, and a biking speed of 10 miles per hour, and completes the event in 90 minutes. How long, in miles, is each segment of the race

Answers

Answer 1

Answer:

The run is 4.875 miles long, while, the bike is 6.875 miles long.

Step-by-step explanation:

Let d = running distance and d' = biking distance.

Given that d' = d + 2 and v = running speed = 6 mph and v' = biking speed = 10 mph.

Since time, t = distance/speed, running time, t = running distance/running speed = d/6 and biking time, t' = biking distance/biking time = d'/10 = (d + 2)/10.

Since the total time, t" = 90 minutes = 1.5 hours,

t + t' = t"

So, d/6 + (d + 2)/10 = 1.5

multiplying through by the L.C.M, 30, we have

30 × d/6 + 30 ×(d + 2)/10 = 30 × 1.5

5d + 3(d + 2) = 45

expanding the brackets, we have

5d + 3d + 6 = 45

collecting like terms, we have

8d = 45 - 6

8d = 39

d = 39/8

d = 4.875 miles

d' = d + 2 = 4.875 + 2 = 6.875 miles

So, the run is 4.875 miles long, while, the bike is 6.875 miles long.


Related Questions

What is the balance of 6,000 compounded annually at a rate of 4% for 10 years

Answers

Answer:

the final balance is $8,945

Answer:

8,881.41

Step-by-step explanation:

Tom bought 3 pizza pies for his 4 friends to share equally among themselves.
How much of the pizza will each friend receive?

Answers

answer is 3/4 i hope this helps

Students were asked how many hours they read in a week. Is this a good example of a statistical question? Why or why not?

Yes, this is a good statistical question because a variety of answers are given.
Yes, this is a good statistical question because there are not a variety of answers that could be given.
No, this is not a good statistical question because there are not a variety of answers that could be given.
No, this is not a good statistical question because there are a variety of answers that could be given.

Answers

Answer:

A

Step-by-step explanation:

when asked how many hours you’ve read all week, there are going to be many numbers that you get from different people.

Answer:

i think the answer is C.

Step-by-step explanation:

there's a variety of answers. one student could say 5 hours and another could say 1 hour. there isnt an exact answer.

Suzanne is putting a fence around her rectangular garden. The length of the garden, x, is 4 feet more than the width. The perimeter of the garden is 32 feet. Write an equation to find the length of the garden.

Enter the correct answer in the box.

Answers

Answer:

Length=10 feet

Width=6 feet

Step-by-step explanation:

Let width (W) of the garden is x feet

Then Length=L=4+x feet

Perimeter=P=2(W + L)

P=2(x+x+4)

32=4x+8

4x=32-8

x=24/4=6 feet

W=6 feet

L=10 feet

Can someone please help me with this and can you please include the work/ how to do it I’m stuck and it’s my last problem.

Answers

Gosh so sorry I do not had a math something like that so hard?

Help please I need this ;-;​

Answers

Answer:

1,5

Step-by-step explanation:

can i please get brainliest?

I need help
Who is here
Wat percentage of (a)30 is 15
B)£1 is 23

Answers

Answer:

(a) is 50%

(b) is 23%

Step-by-step explanation:

15/30 (simplify)

15 divided by 15 is 1

30 divided by 15 is 2

Write that as a fraction

1/2

A half is 0.50 as a decimal number, multiply 0.50 by 100 and you will get 50.

Your answer is 50%

will upvote



On a coordinate grid, point P is at (5, 2) and point R is at (−3, −4). Points Q and S are a reflection of both points across the x-axis. What are the coordinates of Q and S?

Q(−5, 2), S(3, −4)

Q(−5, −2), S(3, 4)

Q(5, −2), S(−3, 4)

Q(−5, 2), S(−3, 4)

Answers

Answer:

c) Q( 5, -2) , S(-3,4)

P( 5,2) → Q( 5, -2)

Q(-3,-4)→ S(-3,4))

Step-by-step explanation:

Explanation:-

Given points are  P( 5,2) and Q(-3,-4)

Points P and R   reflection  across the x-axis then the co-ordinate point is transformed to  (x,y)→ (x,-y)

P( 5,2) → Q( 5, -2)

Q(-3,-4)→ S(-3,-(-4))

Q(-3,-4)→ S(-3,4))

what is three-sevenths of h

Answers

Answer:

Couldn't tell yah, not full question.

Daniel rollerbladed 3 miles in 12 minutes. At this rate, how many miles will he rollerblade in 1 hour? Show your work.

Answers

Answer:

Daniel is rollerblading at 15 miles per hour

Daniel can go 3 miles in 12 minutes so we do 12÷3 to find out how many minutes it takes to go 1 mile which is 4 now we do 60÷4 to get 15

Alternatively we could do 60÷12 to get 5 then do 3×5 to get 15

Step-by-step explanation:

John has $65 in his piggy bank. He wants to buy a new gaming
system for $257. If he saves $!2 per day, how many days will it be
before he can buy his new gaming system?

Answers

John need to save 2 dollars for 96 days

Answer:

96 days

Step-by-step explanation:

Since he already has $65 we will subtract this from $257. This leaves us with $192 to earn. Dividing $192 by 2 (Because John is getting $2 per day) will result in 96.

Write an equation for the line with a y-intercept of 5
that is perpendicular to the line with equation
y=-3x+2.

Answers

Answer:

y = -1/3 x + 5

Step-by-step explanation:

The general equation is y = mx + b

You are told that the y intercept is 5. The point is (0,5)

So far the general equation looks like y = mx + 5

Now we have to find m

The given slope of y = 3x + 2 is 3.

The slope is whatever number is in front of the x

Use this formula for the vertical slope

m * m1 = - 1

m1 = 3

3*m = - 1                                     Divide by 3

m = -1/3

So the answer you want is y = -1/3 x + 5

help me plzzzzzzzzzzz​

Answers

Answer:

>\/<

[tex]10[/tex]

>/\<

- remember that the midline is always half of the sum of the other two legs.

here,

UX is the midline,

ST is the leg,

VW is the other leg.

so,

ST + VW = 2UX

now plug in,

25 + VW = 2(35)

25 + VW = 70

VW = 45

request: please mark brainiest, and click the thanks button if correct <3

find the H.C.F of these numbers by continued method 390,205,125​

Answers

Answer:

125, 205, 390

Step-by-step explanation:

Answer:

125​ Supposedly

Step-by-step explanation:

What is the y-intercept of y = - 2x + 6

Answers

Answer:

6

Step-by-step explanation:

slope formula y=mx+b

m=slope

b=y-intercept

Answer:

it's 6

Step-by-step explanation:

y=mx+b

mx is slope

b is the y-intercept

take care

-tired kitten

that really wants to go to sleep forever

Find the slope of the line that passes through the points A (-1,5) and B (7,1).

Answers

Answer:

-1/2

Step-by-step explanation:

A down arrow is drawn with its tip at (2, 0). Then it undergoes a translation described bythe directed line segment (−3, 1). What direction is the arrow pointing?

Answers

Answer:

down

Step-by-step explanation:

In mathematics a when dealing with graphs a translation is basically just moving points left/right and up/down but it does not change the shape of the original figure in any way just moves its position. In this scenario, the down arrow's tip will be moved from point (2,0) to (-3,1) but the arrow will still be the same size and still be pointing downward.

LaTeX: \Delta QRS\cong\Delta TUV,\:QS=3v+2,Δ Q R S ≅ Δ T U V , Q S = 3 v + 2 , and LaTeX: TV=7v-6,T V = 7 v − 6 , enter the lengths of QS

Answers

Answer:

The length of QS = 8

Step-by-step explanation:

From the above question:

Δ Q R S ≅ Δ T U V

Q S = 3 v + 2 , and T V = 7 v − 6 , enter the lengths of QS

Hence:

Step 1

We solve for v

QS = TV

3v + 2 = 7v - 6

Collect like ters

2 + 6 = 7v - 3v

8 = 4v

v = 8/4

v = 2

Step 2

Solving for Q S

Q S = 3 v + 2

v = 2

QS = 3(2) + 2

QS = 6 + 2

QS = 8

The length of QS = 8

HJ and KM are parallel lines.
K
H
N
L
1
M
Which angles are supplementary angles?
JIL and MLN
ZJIL and ZKLI
IL and HIG
OIL and ZHIL

Answers

it's JIL and HIL.

hope it helps :)

The angle ∠JIL and ∠HIL are supplementary angles. Then the correct option is D.

What is an angle?

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

HJ and KM are parallel lines. And NG interset the line HJ at I and KM at L.

Then the supplementary angles are given below.

∠JIL and ∠HIL

The angle ∠JIL and ∠HIL are supplementary angles. Then the correct option is D.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ5

Can someone help me?

Answers

Answer:

Option (3)

Step-by-step explanation:

Let the unknown angle of the triangle measure x°.

By applying cosine rule in the right triangle,

cos(x) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

cos(x) = [tex]\frac{33}{65}[/tex]

x = [tex]\text{cos}^{-1}(\frac{33}{65})[/tex]

x = 59.49°

  ≈ 60°

Therefore, option (3) will be the correct option.

HAAALP 20) POINTS JWNJNHSBNJNJKS

Answers

Answer: E

Step-by-step explanation: since ur in quadrant 3 the y axis is going to be -4 and the x axis will be 3

The fraction: 340 | 3/4

Which quotient equals to the fraction?

A: 3/4 divided by 340

B: 340 divided by 3/4

C: 340/45

D: 340 divided by 75

Answers

Answer:

It's A I hope that helps

Step-by-step explanation:

There are 480 soccer balls on a field. Every hour, half of the balls are put back into the locker room. Write an equation that can be used to find the number of soccer balls remaining on the field at the end of x hours.

Answers

Answer:

[tex]y= 480-0.5x[/tex]

Step-by-step explanation:

Given data

Number of balls= 480

we are told that 50%(half) of the balls are put back every 1

let the number of hours be x

and let the remaining ball be y after x hours

Hence the expression is given as

[tex]y= 480-0.5x[/tex]

PLEASE HELP ME QUICK~~

Answers

Answer:

I don’t really know if I’m correct but I think it’s “the fraction of switch hitting softball players is greater than 1/20”

Step-by-step explanation:

the sum of two numbers is 40.if the greater number is 8 more than the smaller one , find the numbers

Answers

Answer:

16

Step-by-step explanation:

let the smaller no be x so the greater no is 8 + x

soln

8+x + x = 40

8 + 2x = 40

2x = 40-8

2x = 32

x = 32÷2

therefore x = 16

Answer:

16 and 24

Step-by-step explanation:

let the 2 numbers be x and y, x > y , then

x + y = 40 → (1)

x = y + 8 → (2) [ greater number 8 more than smaller ]

Substitute x = y + 8 into (1)

y + 8 + y = 40, that is

2y + 8 = 40 ( subtract 8 from both sides )

2y = 32 ( divide both sides by 2 )

y = 16

Substitute y = 16 into (2)

x = 16 + 8 = 24

The 2 numbers are 16 and 24

The measure of the angles of a triangle are in the extended ratio of 3 : 7 : 10. Find the measures of the angles.
A. 27 degrees, 63 degrees, 90 degrees
B. 30 degrees, 60 degrees, 90 degrees
C. 30 degrees, 70 degrees, 100 degrees
D.33 degrees, 77 degrees, 80 degrees

Answers

Answer:

A. 27 degrees, 63 degrees, 90 degrees.

Step-by-step explanation:

Let the angle of the triangle be x

Given the following data;

3 : 7 : 10 = 3x : 7x : 10x

We know that the sum of the sides of a triangle is equal to 180 degrees.

3x + 7x + 10x = 180

20x = 180

x = 180/20

x = 9

For the first side;

3x = 3 × 9 = 27°

For the second side;

7x = 7 × 9 = 63°

For the third side;

10x = 10 × 9 = 90°

Therefore, the ratio of the angles of the triangle is 27° : 63° : 90°.

Answer:

The measure of the angles of a triangle are in the extended ratio of 3 : 7 : 10. Find the measures of the angles.

A. 27 degrees, 63 degrees, 90 degrees✓

B. 30 degrees, 60 degrees, 90 degrees

C. 30 degrees, 70 degrees, 100 degrees

D.33 degrees, 77 degrees, 80 degrees

A. is the right answer.

Step-by-step explanation:

Let the required angles of the triangle be 3x, 7x and 10x

According to the above problem,

[tex]3x + 7x + 10x = 180 \\ 20x = 180 \\ x = \frac{180}{20} \\ \boxed{x = 9}[/tex]

Therefore the angles are :---

[tex]3x = 3 \times 9 = 27°✓ \\ 7x = 7 \times 9 = 63°✓ \\ 10x = 10 \times 9 = 90°✓[/tex]

please please help i don’t get this at alllll

If –3(y - 1) = 9, find the value of 1/2y

Answers

Answer:

The value of [tex]\frac{1}{2}y[/tex] is -1

Step-by-step explanation:

Equations

We have the equation:

[tex]-3(y - 1) = 9[/tex]

It's required to find

[tex]\frac{1}{2}y[/tex]

Let's solve the equation. Dividing by -3:

[tex]y - 1 = \frac{9}{-3}= -3[/tex]

Adding 1:

[tex]y=-3+1=-2[/tex]

Since y=-2, then y/2=-1

The value of [tex]\frac{1}{2}y[/tex] is -1

At the beginning of 2010, City A had a population of 2,425 and was growing by 27 residents per year. City B had a population of 1,813 and was growing by 63 residents per year. If this trend continues in what year will the populations of the two cities be the same?

Answers

Answer: 17 years

Step-by-step explanation:

City A is currently 2,425 people in number and growing at 27 per year.

An expression to find the population in a given year assuming the year is x would be:

= 2,425 + 27 * x

= 2,425 + 27x

Applying the same logic to City B would give an expression of:

= 1,813 + 63x

Equating these together will give the year they will be the same:

2,425 + 27x = 1,813 + 63x

2,425 - 1,813 = 63x - 27x

612 = 36x

x = 612/36

x = 17 years

Answer:

gey

Step-by-step explanation:

geyehnr

The graph shows the relationship between the number of pounds of oranges purchased and the total cost of the oranges

Answers

Answer:

nice

Step-by-step explanation:

If m ∠1 = 110°, What is m∠4

PLS HELP ASAP

Answers

Answer:

[tex]\displaystyle 70°[/tex]

Step-by-step explanation:

Consecutive Exteriour Angles form a linear pair, so you set them equal to [tex]\displaystyle 180°:[/tex]

[tex]\displaystyle 180° = 110° + m∠4; 70° = m∠4[/tex]

I am joyous to assist you at any time.

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