SOLUTION: Mary drove to the train station and back. It took two hours less time to get there than it did to get back. The average s[ed on the trip there was 50 mph. The average speed on the

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Question 785534: Mary drove to the train station and back. It took two hours less time to get there than it did to get back. The average s[ed on the trip there was 50 mph. The average speed on the way back was 30mph. How many hours did the trip there take?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
t = hours takem for the round trip
r = hours taken for the return trip
t=r%2B%28r-2%29-->t=2r-2-->t%2B2=2r-->r=%28t%2B2%29%2F2
d = distance to the station = distance traveled back from the station
For the round trip we know that
50t=2d
For the return trip we know that
d=30%28%28t%2B2%29%2F2%29-->d=30%28t%2B2%29%2F2-->d=15%28t%2B2%29-->d=15t%2B30
Substtituting that expression for d into 50t=2d we get
50t=2%2A%2815t%2B30%29-->50t=30t%2B60-->50t-30t=60-->20t=60-->highlight%28t=3%29
Unfortunately, what that means for the trip distances and speeds is scary:
2d=50%2A3-->2d=150-->d=150%2F2=75
r=%283%2B2%29%2F2-->r=2.5
If the trip back took 2.5 hours and the trip to the station took 2hours less,
2.5h-2h=0.5h,
Mary drove the 75 miles to the station in 0.5 hours.
Her average speed when going to the station was
75miles%2F%28%220.5+hours%22%29=150mph