SOLUTION: A bus took a 13-hour trip and traveled 646 miles. The speed was 40 mph for the first part of the trip, and then increased to 58 mph for the second part of the trip. How many hours

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Question 1089678: A bus took a 13-hour trip and traveled 646 miles. The speed was 40 mph for the first part of the trip, and then increased to 58 mph for the second part of the trip. How many hours were traveled at each speed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs traveled at 40 mi/hr
+13+-+t+ = time in hrs traveled at 58 mi/hr
Let +d+ = distance in miles traveled at 40 mi/hr
+646+-+d+ = distance in miles traveled at 58 mi/hr
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(1) +d+=+40t+
(2) +646+-+d+=+58%2A%28+13+-+t+%29+
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(2) +646+-+d+=+754+-+58t+
(2) +d+=+58t+-+108+
Plug (1) into (2)
(2) +40t+=+58t+-+108+
(2) +18t+=+108+
(2) +t+=+6+
and
+13+-+t+=+13+-+6+
+13+-+t+=+7+
-----------------------
traveled for 6 hrs at 40 mi/hr
traveled for 7 hrs at 58 mi/hr
-------------------------------
check:
(1) +d+=+40t+
(1) +d+=+40%2A6+
(1) +d+=+240+
and
(2) +646+-+d+=+58%2A%28+13+-+t+%29+
(2) +646+-+d+=+58%2A7+
(2) +d+=+646+-+406+
(2) +d+=+240+
OK