SOLUTION: Carlos and Maria drove a total of 258 miles in 5 hrs. Carlos drove the first part and averaged 53 mph. Maria drove the remainder of the trip and averaged 51 mph. How many hours did

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Question 950675: Carlos and Maria drove a total of 258 miles in 5 hrs. Carlos drove the first part and averaged 53 mph. Maria drove the remainder of the trip and averaged 51 mph. How many hours did Maria drive. Answer can be rounded to the nearest tenth ..
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance in miles Carlos drove
Let +t+ = time in hrs that Carlos drove
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Carlos's equation:
(1) +d+=+53t+
Maria's equation:
(2) +258+-+d+=+51%2A%28+5-t+%29+
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Substitute (1) into (2)
(2) +258+-+53t+=+51%2A%28+5-t+%29+
(2) +258+-+53t+=+255+-+51t+
(2) +2t+=+3+
(2) +t+=+3%2F2+
----------------
Maria drove +5-t+ hrs
+5+-+t+=+5+-+3%2F2+
+5+-+t+=+3.5+
Maria drove 3.5 hrs
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check answer:
(1) +d+=+53t+
(1) +d+=+53%2A%283%2F2%29+
(1) +d+=+79.5+ mi
and
(2) +258+-+d+=+51%2A%28+5-t+%29+
(2) +258+-+79.5+=+51%2A%28+5-3%2F2+%29+
(2) +178.5+=+51%2A3.5+
(2) +178.5+=+178.5+
OK