SOLUTION: Peter drove a distance of 189 miles. Part of the time he averaged 65 miles per hour, and for the remaining time, he averaged 55 miles per hour. The entire trip took 3 hours. How lo

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Peter drove a distance of 189 miles. Part of the time he averaged 65 miles per hour, and for the remaining time, he averaged 55 miles per hour. The entire trip took 3 hours. How lo      Log On

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Question 690247: Peter drove a distance of 189 miles. Part of the time he averaged 65 miles per hour, and for the remaining time, he averaged 55 miles per hour. The entire trip took 3 hours. How long did he travel at each rate?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance traveled at +65+ mi/hr
+189+-+d+ = the distance traveled at +55+ mi/hr
Let +t+ = his time spent traveling at +65+ mi/hr
+3-+t+ = his time spent traveling at +55+ mi/hr
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Equation for +65+ mi/hr:
(1) +d+=+65t+
Equation for +55+ mi/hr:
(2) +189+-+d+=+55%2A%28+3+-+t+%29+
-------------------------
(2) +189+-+d+=+165+-+55t+
Substitute (1) into (2)
(2) +189+-+65t+=+165+-+55t+
(2) +65t+-+55t+=+189+-+165+
(2) +10t+=+24+
(2) +t+=+2.4+
+.4%2A60+=+24+
+3+-+2.4+=+.6+
+.6%2A60+=+36+
He spent 2 hrs and 24 min traveling at +65+ mi/hr
He spent 36 min traveling at +55+ mi/hr
check answer:
(2) +189+-+d+=+55%2A%28+3+-+t+%29+
(2) +189+-+d+=+55%2A%28+3+-+2.4+%29+
(2) +189+-+d+=+.6%2A55+
(2) +d+=+189+-+33+
(2) +d+=+156+
and
(1) +d+=+65t+
(1) +d+=+65%2A2.4+
(1) +d+=+156+
OK