SOLUTION: A motorboat can maintain a constant speed of 16 miles per hour in still water. The boat makes a certain trip upstream in 20 minutes; the return trip takes 15 minutes. What is the s

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Question 769712: A motorboat can maintain a constant speed of 16 miles per hour in still water. The boat makes a certain trip upstream in 20 minutes; the return trip takes 15 minutes. What is the speed of the current?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the speed of the current
Let +d+ = the one-way distance of the trip
You must convert the minutes to hours
-------------
Going upstream:
(1) +d+=+%28+16+-+c+%29%2A%28+20%2F60+%29+
Going downstream:
(2) +d+=+%28+16+%2B+c+%29%2A%28+15%2F60+%29+
---------------------------
Substitute (1) into (2)
(2) +%28+16+-+c+%29%2A%28+20%2F60+%29+=+%28+16+%2B+c+%29%2A%28+15%2F60+%29+
(2) +%28+16+-+c+%29%2A%28+1%2F3+%29+=+%28+16+%2B+c+%29%2A%28+1%2F4+%29+
Multiply both sides by +12+
(2) +4%2A%28+16+-+c+%29+=+3%2A%28+16+%2B+c+%29+
(2) +64+-+4c+=+48+%2B+3c+
(2) +7c+=+16+
(2) +c+=+16%2F7+ mi/hr
---------------
check:
(2) +d+=+%28+16+%2B+16%2F7+%29%2A%28+15%2F60+%29+
(2) +d+=+16%2A%28+1+%2B+1%2F7+%29%2A%28+1%2F4+%29+
(2) +d+=+4%2A%28+8%2F7+%29+
(2) +d+=+32%2F7+
and
(1) +d+=+%28+16+-+16%2F7+%29%2A%28+20%2F60+%29+
(1) +d+=+16%2A%28+1+-+1%2F7+%29%2A%28+1%2F3+%29+
(1) +d+=+16%2A%28+6%2F7+%29%2A%281%2F3+%29+
(1) +d+=+16%2A%28+2%2F7+%29+
(1) +d+=+32%2F7+
OK