Question

A remote control car races down the street at 26 miles per hour. Two hours later a second remote control car races straight down the same street at 52 miles per hour in pursuit of the first car. From the moment the first car started, how many hours will it take for the second car to catch up to the first car? what is a reasonable first step in solving this problem?

Answer 1

4 hours

Explanation:

Given

Car 1:

`Speed = 26mph`

`Time = h`

Car 2:

`Speed = 52mph`

`Time = h - 2` --- i.e. 2 hours after car 1

Required

Determine the time car 1 will meet car 2

To do this, we calculate the distance of both cars using:

`Distance = Speed * Time`

For Car 1:

`Distance = 26 * h`

`Distance = 26h`

For Car 2:

`x^(2) Distance = 52 * (h - 2)`

Open bracket

`Distance = 52h - 104`

When car 2 meets up with car 1, they are at the same distance.

So:

`26h = 52h - 104`

Collect Like Terms

`26h - 52h = -104`

`-26h = -104`

Solve for h

`h = (-104)/(-26)`

`h = 4`

Car 2 will catch car 1; 4 hours from the start