Question

16. A truck traveling 45 miles per hour and a train traveling 60 miles per hour cover the same distance. The truck travels 2 hours longer than the train. How many hours does each travel?

What equation would represent the total distance traveled by both the train and the truck? [Hint: Remember the distance traveled formula d = rt.]

A. 105x + 90
B. 105x
C. 45x + 90
D. 60x

Answer 1

The equation representing the total distance would be A. 105x + 90.

The time the truck has travelled would be 8 hours while the time traveled by the train would be 6 hours.

Explanation:

Firstly, let's set the time travelled by the train to be x hours.

According to the question, the equation would be 45(x + 2) = 60x, because the truck has travelled 2 more hours than the train.

Hence:

`45(x + 2) = 60x`

`45x + 90 = 60x`

`90 = 60x - 45x`

`15x = 90`

`x = 6`

Therefore, the truck has travelled a total of (6 + 2) hours = 8 hours, and the train has travelled for 6 hours.

Also, the equation can be found by adding both equations up:

`45(x + 2) + 60x`

`= 45x + 90 + 60x`

`= 105x + 90`

Hope this helped!