Question

Two cars travel at the same speed to different destinations. Car A reaches its destination in 17 minutes. Car B reaches its destination in 32 minutes. Car B travels 12 miles farther than Car A. How fast do the cars travel?

Answer 1

speed of car A =Speed of car B=0.8 miles/minutes.

Explanation:

We are given that speed of car A is equal to speed of car B.

Also let car A travels x miles.

and car B travels y miles.

Car A reaches its destination in 17 minutes.

this means that speed of car A is given by:
`(x)/(17)` miles/minutes ( since speed is defined as the ratio of distance and time).

Car B reaches its destination in 32 minutes.

This means that the speed of car B is given by:
`(y)/(32)` miles/minutes

as speed of both cars are equal this means:

`(x)/(17)=(y)/(32)`------(1)

Also we are given Car B travels 12 miles farther than Car A.

this means
`y-x=12`

`y=12+x`------(2)

on using equation (1) and (2) we have:

`(x)/(17)=(12+x)/(32)\\  \\32x=17(12+x)\\\\32x=17*12+17x\\\\32x-17x=17*12\\\\15x=122*17\\\\x=13.6`

Hence the speed of car A is 0.8 miles/minutes ( since x/17 is the speed of car A)

Speed of car B=0.8 miles/minutes.