Question

A freight train travels 210 miles in the same amount of time a car travels 330 miles. If the

rate of the car is 20 mph more than the rate of the train, find the rate of each.

Answer 1

35 mph, 55 mph

Explanation:

speed = distance / time

time = distance / speed

Since the time taken by the train and the car are the same, we can...

1. use x and x + 20 for the speeds, respectively

2. divide the respective distances and speeds, and since they're equal (time), we can form the equation

`(210)/(x)=(330)/(x+20)\\`

then, we solve for x

`210\left(x+20\right)=330x`

`210x+4200=330x`

`120x=4200`

`x=(4200)/(120)`

`x=35\\`

The train travels at a rate of 35 mph, while the car travels 20 mph faster, so 55 mph.