Train race!
Two trains, one
feet long, the other
feet long, on parallel tracks, can pass each other completely in
seconds when moving in opposite directions. When moving in the same direction, the faster train completely passes the slower one in
seconds. Find the speed of the slower train in feet per second.
The answer is 25.
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1 solution
Let f (feet per second) represent the speed of the faster train and s (feet per second), the speed of the slower train. The relative speed when the trains are going in opposite directions is f + s , and relative speed, when they are going in the same direction is f − s . In either case, the distance traveled is 3 5 0 + 4 5 0 = 8 0 0 (feet).
Since (relative) r a t e × t i m e = d i s t a n c e , we have ( f + s ) ( 8 ) = 8 0 0 and ( f − s ) ( 1 6 ) = 8 0 0 . This pair of equations is easily solved, yielding the values f = 7 5 and s = 2 5 (feet per second).