Question

Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 miles per hour and train B is traveling at 80 miles per hour. Train A passes a station at 8:20 p.m. If train B passes the same station at 8:32 p.m., at what time will train B catch up to Train A?

When will train B catch up with Train A?

Answer 1

B-------A---------------|
Train A is at point A at 8:32 while train B is at point B. Train B passes point A at 8:32 or 12 minutes later. 12 minutes is 12/60 = 0.20 hour. How much farther did train B travel? That must be distance = rate x time = 80 mph x 0.2 hr = 16 miles. To catch up, train B must travel the same distance as train A BUT must go 16 miles farther. They will get to the point I've marked | at the same time. How much time does it take each?
Train A, time = d/r = = d/60
Train B, time = (d+16)/80.
Set time = time and
d/60 = (d+16)/80.
Solve for d, then use that to calculate how long it takes for train a to travel that distance, add that to 8:32 and that will be the time both are at the| on my diagram above. If I didn't make a mistake (but check my work), distance is 48 miles and the time it takes A to get there is 0.8 hour or 48 minutes. Add that to 8:32. Again, check my work.