SOLUTION: A ferry moves up and down a river between Town A and B. It takes the ferry two hours to reach Town A and only an hour and thirty minutes to return to Town B. If the river current i

Algebra ->  Length-and-distance -> SOLUTION: A ferry moves up and down a river between Town A and B. It takes the ferry two hours to reach Town A and only an hour and thirty minutes to return to Town B. If the river current i      Log On


   



Question 921283: A ferry moves up and down a river between Town A and B. It takes the ferry two hours to reach Town A and only an hour and thirty minutes to return to Town B. If the river current is 5 mph how far apart are the two cities?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the ferry in still water
Let +d+ = the distance between the towns
(1) +s+-+5+=+d%2F2+ = speed going from B to A
(2) +s+%2B+5+=+d%2F1.5+ = speed going from A to B
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(1) +2s+-+10+=+d+
and
(2) +1.5s+%2B+7.5+=+d+
----------------------
By substitution:
+1.5s+%2B+7.5+=+2s+-+10+
+.5s+=+17.5+
+s+=+35+
and
(1) +2s+-+10+=+d+
(1) +2%2A35+-+10+=+d+
(1) +d+=+70+-+10+
(1) +d+=+60+
The towns are 60 mi apart
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check:
(2) +1.5s+%2B+7.5+=+d+
(2) +1.5%2A35+%2B+7.5+=+60+
(2) +52.5+%2B+7.5+=+60+
(2) +60+=+60+
OK