Question

I need help with this question:

When Clint began his pursuit, Sue was already 60 miles ahead. If Sue travels at 40MPH and Clint travels at 60MPH, how many hours will it take Clint to catch up with Sue?​

Answer 1

In 3 hours Clint will catch up with Sue

Explanation:

Let

x -----> the time in hours

y ----> the distance in miles

Remember that

The speed is equal to divide the distance by the time

so

The distance is equal to multiply the speed by the time

The linear equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem

Clint's equation

The slope is equal to the speed

so

`m=60\ mph`

The y-intercept is equal to 0 miles (at the time x=0, the distance traveled is zero)

`b=0`

substitute

`y=60x` ----> equation A

Sue's equation

The slope is equal to the speed

so

`m=40\ mph`

The y-intercept is equal to 60 miles (at the time x=0, the distance traveled is 60 miles)

`b=60\ miles`

substitute

`y=40x+60` -----> equation B

Equate equation A and equation B

`60x=40x+60`

Solve for x

`60x-40x=60`

`20x=60`

`x=3\ hours`

therefore

In 3 hours Clint will catch up with Sue