Two trains leave a station traveling the same direction. Train A leaves the station traveling at a constant speed of 60 mph, and train B leaves the station traveling at a constant speed of 80 mph. If both trains maintain constant speeds, in how many minutes will train B overtake train A if train A left 40 minutes prior to train B? Choose the correct choice from the following answers
A) 90
B) 100
C) 110
D) 120
E) 130

Rationale: we can use d = rt [ distance = rate * time ] train a will have traveled for 40 minutes longer than train b when b overtakes a , so time of train a : t + 40 minutes = t + ( 2 / 3 ) hours ( use hours since the rate is in hours ) time of train b : t rate of train a : 60 mph rate of train b : 80 mph the distances traveled by each will be equal when train b overtakes train a , so we can set the right sides of d = rt equal for the two trains ( rate of train a ) * ( time of train a ) = ( rate of train b ) * ( time of train b ) 60 * ( t + 2 / 3 ) = 80 * t 60 t + 40 = 80 t 40 = 20 t 2 = t 2 hours = 120 minutes d
Answer: D