distance problem

Question

in the morning the passenger train made the trip in 3 hours. In the afternoon the freight train made the same trip in 7 hours. Find the rate of each in terms of mph if the rate of the freight train was 40 miles per hour less than the rate of the passenger train. Put your answer in the form (P,F)

Answer 1

Distance = rate x time

For passenger train, Distance_p = 3P where P is passenge train's speed in MPH.

For freight, Distance_f = 7F where F is freight train's speed.

It's given that F = P - 40

So, by substitution D_f = 7(P - 40)

The two distances are equal (D_p = D_f), so 3P = 7(P - 40) -> 3P = 7P - 280 (distribution rule)

Solving: 3P - 7P = -280 -> -4P = -280 -> P = 70 MPH

The F = 70 - 40 = 30 MPH

Check: D_p = 70(3) = 210 mi. D_f = 30(7) = 210 mi.