Math Word Problem
posted by amy .
A metra commuter train leaves Union Station in Chicago at 12 noon. Twp hours later an Amtrak train leaves on the same track, traveling at an average speed that is 50 miles per hour faster than the Metra train. At 3PM the Amtrak train is 10 miles behind the commuter train. How fast is each going?
I don't understand how to solve this.
I only know how to solve it if the problem has the velocity for both.
Please could someone write the equation

let A = speed of Amtrak train
let M=speed of Metro train
so we can write A=M+50
as A is travelling 50 mph faster than M
as there are two unknowns we need another equation
at 3pm distance travelled by A is Ax1 or 1A miles
at 3pm distance travelled by M is Mx3 miles
but A is 10 miles behind M so
3M10=1A
we now have two equations so we can solve these for A and M. 
I solved it got the right answer but what about the 2hours part?

A train leaves the station at 7:00 A.M. traveling west at 80 mi/h. On a parallel track, a second train leaves the station 3 hours later traveling west a 100 mi/h. At what time will the second train catch up with the first? 29
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