SOLUTION: Leah went to the internet cafe traveling 20 mph and returned home traveling 10 mph. If the total trip took 6 hours, how long did Leah travel at each speed?

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Question 1046112: Leah went to the internet cafe traveling 20 mph and returned home traveling 10 mph. If the total trip took 6 hours, how long did Leah travel at each speed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs going TO the cafe
+6+-+t+ = time in hrs returning FROM cafe
Let +d+ = the one-way distance to cafe
---------------------------------------
Going to cafe:
(1) +d+=+20t+
Returning from cafe:
(2) +d+=+10%2A%28+6-t+%29+
----------------------
Plug (1) into (2)
(2) +20t+=+10%2A%28+6-t+%29+
(2) +20t+=+60+-+10t+
(2) +30t+=+60+
(2) +t+=+2+ hrs
and
+6+-+t+=+6+-+2+
+6+-+t+=+4+ hrs
------------------
Leah took 2 hrs going 20 mi/hr
Leah took 4 hrs going 10 mi/hr
-----------------------------
check:
(1) +d+=+20t+
(1) +d+=+20%2A2+
(1) +d+=+40+ mi
and
(2) +d+=+10%2A%28+6-t+%29+
(2) +d+=+10%2A%28+6-2+%29+
(2) +d+=+10%2A4+
(2) +d+=+40+ mi
OK