Have a Uniform Motion question

* * A Metra commuter

train leaves Union Station in Chicago at

12:00 noon. Two hours later an Amtrak

train leaves on the same track traveling

at an average speed that is 50 mph faster than the Metra train. At 3pm the Amtrak train is 10 miles behind the commuter

train. How fast is each

going?

Let x mph be the speed that the commuter train is travelling with. The speed of the Amtrak train is (x+50) mph. Let y be the distance the commuter train travels from 12:00 noon to 3 pm, that is in 3 hours. The distance the Amtrak train travels from 2pm to 3pm, that is in 1 hour is (y-10) miles. As distance = speed x time, we have:

y - 10 = (x+50) x 1

y = 3x

Substituting for y in the first equation, we have:

3x - 10 = x + 50, 2x = 60, x = 30mph

So the speed of the commuter train is 30 mph and that of the Amtrak train is (50+30) mph = 80 mph