SOLUTION: A bus service runs between two cities. Going one way, the average speed of the bus is 66mph, and going the other way, it is 3mph slower, so the ride takes 20 minutes longer. What i

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A bus service runs between two cities. Going one way, the average speed of the bus is 66mph, and going the other way, it is 3mph slower, so the ride takes 20 minutes longer. What i      Log On

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Question 891416: A bus service runs between two cities. Going one way, the average speed of the bus is 66mph, and going the other way, it is 3mph slower, so the ride takes 20 minutes longer. What is the distance between the two cities?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hours to travel at +66+ mi/hr
+t+%2B+20%2F60+=+t+%2B+1%2F3+ = time in hours to travel at +66+-+3+=+63+ mi/hr
Let +d+ = the distance in miles between the cities
--------------------
Traveling at +66+ mi/hr:
(1) +d+=+66t+
Traveling at +63+ mi/hr:
(2) +d+=+63%2A%28+t+%2B+1%2F3+%29+
------------------------
Substitute (1) into (2)
(2) +66t+=+63%2A%28+t+%2B+1%2F3+%29+
(2) +66t=+63t+%2B+21+
(2) +3t+=+21+
(2) +t+=+7+
and, since
(1) +d+=+66t+
(1) +d+=+66%2A7+
(1) +d+=+462+
The distance between the cities is 462 mi
check:
(2) +d+=+63%2A%28+t+%2B+1%2F3+%29+
(2) +462+=+63%2A%28+7+%2B+1%2F3+%29+
(2) +462+=+441+%2B+21+
(2) +462+=+462+
OK