SOLUTION: The speed of a current is 6 mph. If a boat travels 52 miles downstream in the same time that it takes to travel 26 miles upstream, what is the speed of the boat in still water?

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Question 753546: The speed of a current is 6 mph. If a boat travels 52 miles downstream in the same time that it takes to travel 26 miles upstream, what is the speed of the boat in still water?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the boat in still water
+s+%2B+6+ = the speed of the boat going with the current
+s+-+6+ = the speed of the boat going against the current
Let +t+ = the time for both trips
------------------------------
Equation for going downstream:
(1) +52+=+%28+s%2B6+%29%2At+
Equation for going upstream:
(2) +26+=+%28+s-6+%29%2At+
-------------------
(1) +s%2At+%2B+6t+=+52+
and
(2) +s%2At+-+6t+=+26+
(2) +s%2At+=+6t+%2B+26+
(2) +s+=+6+%2B+26%2Ft+
-------------------
Substitute (2) into (1)
(1) +%28+6+%2B+26%2Ft+%29%2At+%2B+6t+=+52+
(1) +6t+%2B+26+%2B+6t+=+52+
(1) +12t+=+26+
(1) +t+=+13%2F6+ hrs
and, since
(2) +s+=+6+%2B+26%2Ft+
(2) +s+=+6+%2B+26%2F%28%28+13%2F6%29%29+
(2) +s+=+6+%2B+12+
(2) +s+=+18+
The speed of the boat in still water is 18 mi/hr
check:
(1) +52+=+%28+s%2B6+%29%2At+
(1) +52+=+%28+18%2B6+%29%2At+
(1) +52+=+24t+
(1) +t+=+52%2F24+
(1) +t+=+13%2F6+
and
(2) +26+=+%28+s-6+%29%2At+
(2) +26+=+%28+18-6+%29%2At+
(2) +26+=+12t+
(2) +t+=+26%2F12+
(2) +t+=+13%2F6+
OK