SOLUTION: Ronald made a trip of 450 miles in 8 hours. Before noon he averaged 60 miles per hour, and after noon he averaged 50 miles per hour. At what time did he begin his trip and when did

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Question 683358: Ronald made a trip of 450 miles in 8 hours. Before noon he averaged 60 miles per hour, and after noon he averaged 50 miles per hour. At what time did he begin his trip and when did he end it?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hours spent before noon
+8+-+t+ = time in hours spent after noon
Let +d+ = distance he traveled before noon
+450+-+d+ = distance he traveled after noon
----------------------------------------
Equation before noon:
(1) +d+=+60t+
Equation after noon:
(2) +450+-+d+=+50%2A%28+8+-+t+%29+
-------------------------
Substitute (1) into (2)
(2) +450+-+60t+=+50%2A%28+8+-+t+%29+
(2) +450+-+60t+=+400+-+50t+%29+
(2) +10t+=+450+-+400+
(2) +10t+=+50+
(2) +t+=+5+
-------------
He spent 5 hrs before noon, so he started at
+12+-+5+=+7+, 7 AM
He spent +8+-+t+=+8+-+5+, or 3 hrs after noon
So he finished at 3 PM
check answer:
(1) +d+=+60t+
(1) +d+=+60%2A5+
(10 +d+=+300+
and
(2) +450+-+d+=+50%2A%28+8+-+t+%29+
(2) +450+-+d+=+50%2A%28+8+-+5+%29+
(2) +450+-+d+=+150+
(2) +d+=+450+-+150+
(2) +d+=+300+
OK