how fast is each train traveling if the passenger train passes the freight train in 4 hours?

Question

A freight train leave the train station 4 hours before a passenger train. if the rate of the passenger train is 40 mph faster than the freight train, how fast is each train traveling if the passenger train passes the freight train in 4 hours?

Answer 1

The freight train has a speed v_f and the passenger train has a peed of v_p=40+v_f. The distance each train travelled at the point they pass each other is given by d. And the time the freight train travelled is 8; the passenger train waited 4 hours and travelled for 4 hours.

Since speed= distance/time, in other words, d= vt

4v_p = 8v_f

4(40+v_f)=8v_f

40+v_f=2v_f

v_f  = 40mph

v_p = v_f +40 = 80mph