SOLUTION: A cyclist traveled at a rate of 24mph to visit a nearby town. The cyclist averaged 18mph on the return trip. If the round trip took 4.9 hours, find the distance to the nearby tow

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Question 136601: A cyclist traveled at a rate of 24mph to visit a nearby town. The cyclist averaged 18mph on the return trip. If the round trip took 4.9 hours, find the distance to the nearby town.
I am not sure how to work this one. I know that D=R(T). But I am confused because I have a combined round trip time instead of a time going and a time coming back.
Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
Time for outbound trip: t%5B1%5D
Time for return trip: t%5B2%5D
Distance to/from destination: d

For the outbound trip: d=24t%5B1%5D, but that can be expressed as t%5B1%5D=d%2F24
For the return trip: t%5B2%5D=d%2F18

But t%5B1%5D%2Bt%5B2%5D=4.9, so %28d%2F24%29%2B%28d%2F18%29=4.9

LCD for 24 and 18 is 72 (3 * 24 = 4 * 18 = 72)

3d%2F72%2B4d%2F72=4.9

7d=4.9%2A72

d=.7%2A72=50.4

Check:
Outbound trip: t%5B1%5D=50.4%2F24=2.1h
Return trip: t%5B2%5D=50.4%2F18=2.8h

t%5B1%5D%2Bt%5B2%5D=2.1%2B2.8=4.9 Answer checks.