SOLUTION: Micaela drove from Los Angeles to Ventura during rush hour at an average speed of 45miles per hour, and then drove back the same way at an average speed of 30miles per hour. If th

Algebra ->  Linear-equations -> SOLUTION: Micaela drove from Los Angeles to Ventura during rush hour at an average speed of 45miles per hour, and then drove back the same way at an average speed of 30miles per hour. If th      Log On


   

Question 1092563: Micaela drove from Los Angeles to Ventura during rush hour at an average speed of 45miles per hour, and then drove back the same way at an average speed of 30miles per hour.
If the round trip took 3 hour and 15 minutes, how many miles is Micaela's one-way trip from Ventura to Los Angeles?
If the answer is not an integer, enter it as an exact decimal.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs for LA to Ventura trip
+3.25+-+t+ = time in hrs for return trip
Let +d+ = one-way distance in miles
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LA to Ventura:
(1) +d+=+45t+
Ventura to LA:
(2) +d+=+30%2A%28+3.25+-+t+%29+
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Plug (1) into (2)
(2) +45t+=+30%2A%28+3.25+-+t+%29+
(2) +45t+=+97.5+-+30t+
(2) +75t+=+97.5+
(2) +t+=+1.3+ hrs
-----------------------
(1) +d+=+45%2A1.3+
(1) +d+=+58.5+ mi
Her one-way trip was 58.5 mi
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check answer:
(2) +d+=+30%2A%28+3.25+-+1.3+%29+
(2) +d+=+97.5+-+39+
(2) +d+=+58.5+ mi
OK