SOLUTION: Mark made a business trip of 339.5 miles. He averaged 56 mph for the first part of the trip and 57 mph for the second part. If the trip took 6 hours, how long did he travel at ea

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Mark made a business trip of 339.5 miles. He averaged 56 mph for the first part of the trip and 57 mph for the second part. If the trip took 6 hours, how long did he travel at ea      Log On

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Question 1054145: Mark made a business trip of 339.5 miles. He averaged 56 mph for the first part of the trip and 57 mph for the second part. If the trip took 6 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+ = distance in miles traveled
on the 1st part of the trip
+339.5+-+d+ = distance in miles traveled
on the 2nd part of the trip
Let +t+ = time in hrs for 1st part of the trip
+6+-+t+ = time in hrs for the 2nd part of the trip
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Equation for the 1st part:
(1) +d+=+56t+
Equation for the 2nd part:
(2) +339.5+-+d+=+57%2A%28+6+-+t+%29+
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(2) +339.5+-+d+=+342+-+57t+
Plug (1) into (2)
(2) +339.5+-+56t+=+342+-+57t+
(2) +57t+-+56t+=+342+-+339.5+
(2) +t+=+2.5+
and
+6+-+t+=+6+-+2.5+
+6+-+t+=+3.5+
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He traveled for 2.5 hrs at 56 mi/hr
He traveled for 3.5 hrs at 57 mi/hr
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check:
(1) +d+=+56t+
(1) +d+=+56%2A2.5+
(1) +d+=+140+ mi
and
(2) +339.5+-+d+=+57%2A%28+6+-+2.5+%29+
(2) +339.5+-+d+=+342+-+142.5+
(2) +d+=+339.5+-+342+%2B+142.5+
(2) +d+=+482+-+342+
(2) +d+=+140+ mi
OK