A passenger train leaves a train depot two hours after a freight train leaves the same depot. The freight train is traveling 16 mph slower than the passenger train. Find the rate of the freight train if the passenger train overtakes the freight train after 3.75 h.
A) 26 mph
B) 50 mph
C) 30 mph
D) 42 mph
E) 54 mph

Question

Quizplus · Accepted Answer

Let the rate of the freight train be x mph.
Then, the rate of the passenger train is (x+16) mph.
Let the distance traveled by both the trains be the same when the passenger train overtakes the freight train, which is d.
Distance traveled by the freight train in 3.75 hours = d
Distance traveled by the passenger train in 3.75 hours + 2 hours (time difference) = d
=> (x+16)*5.75 = x*3.75
=> 5.75x + 92 = 3.75x
=> 2x = 92
=> x = 46
Therefore, the rate of the freight train = x = 46 mph.

A Passenger Train Leaves a Train Depot Two Hours After