SOLUTION: Trains A and B are traveling in the same direction on parallel lines. Train A is traveling at 40 miles per hour and Train B is traveling 50 miles an hour. Than Train A passes a st

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Question 148282: Trains A and B are traveling in the same direction on parallel lines. Train A is traveling at 40 miles per hour and Train B is traveling 50 miles an hour. Than Train A passes a station at 12:25 PM. If Train B passes the same station at 12:35 PM. What time will B catch up with Train A? When will Train B catch up with Train A?
When will Train B catch up to Train A?
Time ??? PM or AM?
Thanks
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Imagine that I am a passenger on train B. I have a stopwatch and a very
accurate clock too. I've got a cell phone and I'm in contact with
someone at the station
I know the seed of train A and train B also.
I tell the station "Let me know exactly when train A passes the station"
They tell me "Train A just passed"
My clock tells me it's 12:25
Then my train, train B, passes the station.
My clock says it's 12:35. I start my stopwatch
10 minutes have passed, or of an hour and since

mi
That's how far train A is from the station when I go past the station.
I know train A is mi ahead of me, but when I stop the
stopwatch we will be side by side.
Let = time from start to stop
= the distance I have to go to meet train A
is the distance train A has to go to meet me
For A:

For B:

Substitute the 2nd equation into the 1st

multiply both sides by

hr or min
If I started my stopwatch at 12:35 PM, then the trains meet
at 1:15 PM answer
check answer:

mi
Train A covers this distance (station to meeting) in
hr

OK