SOLUTION: A motorist averaged 670 miles in 12 hours. Before 4 pm, he averaged 60 mph and after 4 pm he averaged 50 mph. At what time did he begin his trip and at what time did he end it?

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Question 1014272: A motorist averaged 670 miles in 12 hours. Before 4 pm, he averaged 60 mph and after 4 pm he averaged 50 mph. At what time did he begin his trip and at what time did he end it?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance in miles he covered before 4 PM
+670+-+d+ = distance in miles he covered after 4 PM
Let +t+ = time of trip before 4 PM
+12+-+t+ = time of trip after 4 PM
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Equation before 4 PM:
(1) +d+=+60t+
Equation after 4 PM:
(2) +670+-+d+=+50%2A%28+12+-+t+%29+
----------------------------
Substitute (1) into (2)
(2) +670+-60t+=+50%2A%28+12+-+t+%29+
(2) +670+-60t+=+600+-+50t+
(2) +10t+=+670+-+600+
(2) +10t+=+70+
(2) +t+=+7+
and
+12+-+t+=+5+
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7 hrs before 4 PM is 9AM
5 hrs after 4 PM is 9 PM
----------------------
He began at 9AM and ended at 9 PM
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check:
(1) +d+=+60t+
(1) +d+=+60%2A7+
(1) +d+=+420+
and
(2) +670+-+d+=+50%2A%28+12+-+t+%29+
(2) +670+-+d+=+50%2A%28+12+-7+%29+
(2) +670+-+d+=+250+
(2) +d+=+670+-+250+
(2) +d+=+420+
OK