What is the rate of the trains?

Question

Train A and train B leave a central station at the same time. They travel the same speed, but in opposite directions, with train A heading towards station A, and train B heading towards station B. Train A reaches station A after 3 h. Train B reaches station B after 21/4 h. Station A and Station B are 420 mi apart. What is the rate of the trains?

Answer 1

Distance = (Rate)(Time)

Let x = rate of each train

Distance traveled by train A = 3x

Distance traveled by train B = 5.25x

3x + 5.25x = 420

8.25x = 420

x = 50.9 mph

Answer 2

TrainA=v*3t=dA

TrainB=v*5.25t=dB

dA+dB=420

2v*8.25=420

2v=50.91

v=25.455mph