SOLUTION: Jane leaves her house and drives in a straight line at a speed of 42 mph. Her speed on the return trip is 52 mph. The trip back home takes 15 minutes less than the outbound trip. W

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Jane leaves her house and drives in a straight line at a speed of 42 mph. Her speed on the return trip is 52 mph. The trip back home takes 15 minutes less than the outbound trip. W      Log On

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Question 731491: Jane leaves her house and drives in a straight line at a speed of 42 mph. Her speed on the return trip is 52 mph. The trip back home takes 15 minutes less than the outbound trip. What was Jane's total travel time in hours?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+%7D%7D+=+the+one-way+distance+for+her+trip+in+miles%0D%0ALet+%7B%7B%7B+t+ = the time spent driving at 42 mi/hr in hrs
+t+-+1%2F4+ = time spent driving at 52 mi/hr in hrs
-------------
Equation for leaving house:
(1) +d+=+42t+
Equation for coming back:
(2) +d+=+52%2A%28+t+-+1%2F4+%29+
----------------------
By substitution:
+42t+=+52%2A%28+t+-+1%2F4+%29+
+42t+=+52t+-+26%2F2%0D%0A%7B%7B%7B+42t+=+52t+-+13+
+10t+=+13+
+t+=+1.3+
+t+-+1%2F4+=+1%2B+6%2F20+-+5%2F20+
+t+-+1%2F4+=+1+%2B+1%2F20+
-------------------
Jane's total time is +1+%2B+6%2F20+%2B+1+%2B+1%2F20+
+2+%2B+7%2F20+
+%287%2F20%29%2A60+=+21+
2 hours and 21 minutes total
------------------------
check answer:
(1) +d+=+42t+
(1) +d+=+42%2A1.3+
(1) +d+=+54.6+
and
(2) +d+=+52%2A%28+t+-+1%2F4+%29+
(2) +d+=+52%2A%28+26%2F20+-+5%2F20+%29+
(2) +d+=+52%2A%2821%2F20%29+
(2) +d+=+54.6+
OK