SOLUTION: Quinn has 5 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down.

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Question 1050182: Quinn has 5 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 9 mph and walks back at a speed of 3 mph, how long should she plan to spend walking back?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs spent running
+5+-+t+ = time in hrs spent walking
Let +d+ = the one-way distance she runs
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Equation for running:
(1) +d+=+9t+
equation for walking:
(2) +d+=+3%2A%28+5+-+t+%29+
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Substitute (1) into (2)
(2) +9t+=+3%2A%28+5+-+t+%29+
(2) +9t+=+15+-+3t+
(2) +12t+=+15+
(2) +t+=+5%2F4+ hrs
and
+5+-+t+=+5+-+5%2F4+
+5+-+t+=+20%2F4+-+5%2F4+
+5+-+t+=+15%2F4+ hrs
+15%2F4+=+3+%2B+3%2F4+
She should plan on 3 hrs and 45 min for walking
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check answer:
(1) +d+=+9t+
(1) +d+=+9%2A%285%2F4%29+
(1) +d+=+45%2F4+ mi
and
(2) +d+=+3%2A%28+5+-+t+%29+
(2) +d+=+3%2A%28+5+-+5%2F4+%29+
(2) +d+=+15+-+15%2F4+
(2) +d+=+15+-+3+-+3%2F4+
(2) +d+=+12+-+3%2F4+
(2) +d+=+48%2F4+-+3%2F4+
(2) +d+=+45%2F4+
OK