Word problem

"Train A and train B are traveling in the same direction on parallel tracks. Train A is traveling at 100 miles per hour and Train B is traveling at 120 miles per hour. Train A passes a station at 12:25am. If train B passes the same station at 12:40am, what time will train B catch up with train A?"

I'm not really sure where to start to set up my equation(s). If I could get a starting point I would like to try to solve it on my own. Thanks.

Hello, kmgc51106!

Here's a back-door approach . . .

Train A and train B are traveling in the same direction on parallel tracks.
Train A is traveling at 100 miles per hour and Train B is traveling at 120 miles per hour.
Train A passes a station at 12:25 am; train B passes the same station at 12:40 am.
At what time will train B catch up with train A?

Click to expand...

Train A passes the station 15 minute before train B, a quarter-hour headstart.

\(\displaystyle \text{At 100 mph, train A is ahead by: }\:100 \times\tfrac{1}{4} \:=\:25\text{ miles.}\)


\(\displaystyle \text{Train B is ovettaking train A at a speed of: }\:120 - 100 \:=\:20\text{ mph.}\)

\(\displaystyle \text{It is as if train A has }stopped\text{ and train B is appoaching at 20 mph.}\)


\(\displaystyle \text{How long does it take train B to cover the 25 miles?}\)

\(\displaystyle t \:=\:\frac{D}{r} \quad\Rightarrow\quad \frac{\text{25 miles}}{\text{ 20 mph}} \;=\;\frac{5}{4} \;=\;1\tfrac{1}{4}\text{ hours.}\)


\(\displaystyle \text{The time will be: }\;12\!:\!40\text{ am} + 1\!:\!15 \;=\;1:55\text{ pm.}\)