SOLUTION: A fright train passes the Old Towne train station at 11:00 A.M. going 30 mph. Ten minutes later, a passenger train, headed in the same direction on an adjacent track, passes the sa

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Question 700031: A fright train passes the Old Towne train station at 11:00 A.M. going 30 mph. Ten minutes later, a passenger train, headed in the same direction on an adjacent track, passes the same station at 45 mph. At what time will the passenger train catch the fright train?
My book gives an answer as 11:30 A.M., but I get another answer. Can you help, please? Thank you in advance.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
t = time in hours since 11:00 AM
10 minutes = 10%2F60=1%2F6 hours
The distance from Old Towne station after t is
30t for the freight train, and
45%28t-1%2F6%29=45t-45%2F6=45t-7.5 for the passenger train.
When the passenger train catches up to the freight train,
45t-7.5=30t --> 45t-7.5-30t=30t-30y --> 15t-7.5=0 --> 15t-7.5%2B7.5=0%2B7.5 --> 15t=7.5 --> 15t%2F15=7.5%2F15 --> highlight%28t=0.5%29
The passenger train catches up to the freight train 0.5 hours (half an hour, or 30 minutes) after 11:00 AM, at 11:30 AM.