SOLUTION: Jane rides her bike to the lake. Going to the lake, she averages 12mph. On the return trip,she averages 10mph. If the round trip takes a total of 5.5 hours, how long does the re

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Question 310791: Jane rides her bike to the lake. Going to the lake, she averages 12mph. On the return trip,she averages 10mph. If the round trip takes a total of 5.5 hours, how long does the return trip take?
Found 2 solutions by josmiceli, checkley77:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Going to lake:
d+=+r%5B1%5D%2At%5B1%5D
Returning from lake:
d+=+r%5B2%5D%2At%5B2%5D
given:
r%5B1%5D+=+12 mi/hr
r%5B2%5D+=+10 mi/hr
t%5B1%5D+%2B+t%5B2%5D+=+5.5 hrs
--------------------
Going to lake:
d+=+12%2At%5B1%5D
Returning:
d+=+10%2A%285.5+-+t%5B1%5D%29
I can set the right sides equal to eachother
12t%5B1%5D+=+55+-+10t%5B1%5D
22t%5B1%5D+=+55
t%5B1%5D+=+2.5 hrs
t%5B2%5D+=+5.5+-+2.5 hrs
t%5B2%5D+=+3 hrs
The return trip takes 3 hrs

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
D=12T
D=10(5.5-T)
THE DISTANCES ARE EQUAL THUS THE EQUATIONS ARE EQUAL
12T=10(5.5-T)
12T=55-10T
12T+10T=55
22T=55
T=55/22
T=55/22=5/2=2.5 HOURS FOR THE 12 MPH TRIP.
5.5-2.5=3 HOURS FOR THE 10MPH TRIP.
PROOF:
12*2.5=10*3
30=30