Question

A passenger train and a freight train leave San Jose at 3PM, traveling in the same direction. The passenger train is going three times as fast as the freight train. At 6PM they are 240 miles apart. How fast is each travelling?
Pls help me. I am hopeless

Answer 1

Let's say that the speed of the freight train is $x$ and the one of the passenger train is $3x$.

$x$ MPH means every hour the freight train covers $x$ miles., which means in 3h it will have covered 3 times as much: $3x$ mi.

Following the same logic, $3x$ MPH means every hour the passenger train covers $3x$ miles, meaning after 3h it will have covered 3 times as much as well: $9x$ mi.

Now, having expressed those distances and speeds algebraically, we find the difference between the two distances covered after 3h, knowing it will be equal to 240:

$9x-3x=6x\\6x=240\\x=240/6\\x=40$

Knowing this, we can surely affirm that the freight train is travelling at 40MPH and the passenger train is travelling three times as fast, 120MPH.