SOLUTION: train A is traveling at 60 mph and train B at 80 mph. train A passes the station at 810 and train B at 825 at what time will train B catch train A?

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Question 280099: train A is traveling at 60 mph and train B at 80 mph. train A passes the station at 810 and train B at 825 at what time will train B catch train A?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Train A has a 15 minute head start over B if you consider
the station as the starting point. In that time, A has gone
.25%2A60+=+15 miles.
Assume I have a stopwatch. I'll start it when B reaches the station
If I stop it when B catches A, both trains will have been moving
for the same length of time, which I'll call t
given:
v%5Ba%5D+=+60 mi/hr
v%5Bb%5D+=+80 mi/hr
d%5Bb%5D+=+d%5Ba%5D+%2B+15 mi
----------------
Now I can write equations for both trains
d%5Ba%5D+=+60t
d%5Ba%5D+%2B+15+=+80t
By substitution,
60t+%2B+15+=+80t
20t+=+15
t+=+3%2F4 hr
Train B will catch train A in 45 min, or at 8:25 + 45 = 9:05
check answer:
d%5Ba%5D+=+60t
d%5Ba%5D+=+60%2A%283%2F4%29
d%5Ba%5D+=+45 mi
and
d%5Ba%5D+%2B+15+=+80t
d%5Ba%5D+%2B+15+=+80%2A%283%2F4%29
d%5Ba%5D+%2B+15+=+60
d%5Ba%5D+=+45 mi
OK