SOLUTION: Sam can row ten miles downstream in one-third the time he can row six miles upstream. If sam can row five miles per hour in still water, how fast is the current?

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Question 841574: Sam can row ten miles downstream in one-third the time he can row six miles upstream. If sam can row five miles per hour in still water, how fast is 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 in mi/hr
Let +t+ = his time for rowing upstream in hrs
-------------
Equation for rowing upstream:
(1) +6+=+%28+5+-+c+%29%2At+
Equation for rowing downstream:
(2) +10+=+%28+5+%2B+c+%29%2A%281%2F3%29%2At+
----------------------------
(1) +6+=+5t+-+c%2At+
and
(2) +10+=+%285%2F3%29%2At+%2B+%281%2F3%29%2Ac%2At+
(2) +30+=+5t+%2B+c%2At+
---------------------
(2) +c%2At+=+-5t+%2B+30+
(2) +c+=+%28+-5t+%2B+30+%29+%2F+t+
substitute (2) into (1)
(1) +6+=+5t+-+c%2At+
(1) +6+=+5t+-+%28%28+-5t+%2B+30+%29%2Ft+%29%2At+
(1) +6+=+5t+-+%28+-5t+%2B+30+%29+
(1) +6+=+5t+%2B+5t+-+30+
(1) +10t+=+36+
(1) +t+=+3.6+ hrs
and
(1) +6+=+%28+5+-+c+%29%2At+
(1) +6+=+%28+5+-+c+%29%2A3.6+
(1) +5+-+c+=+5%2F3+
(1) +c+=+5+-+5%2F3+
(1) +c+=+10%2F3+
The speed of the current is 3.333 miles/hr
check:
(2) +10+=+%28+5+%2B+c+%29%2A%281%2F3%29%2At+
(2) +10+=+%28+5+%2B+10%2F3+%29%2A%281%2F3%29%2At+
(2) +10+=+%28+25%2F3+%29%2A%281%2F3%29%2At+
(2) +25t+=+90+
(2) +t+=+3.6+ hrs
and
(1) +6+=+%28+5+-+c+%29%2At+
(1) +6+=+%28+5+-+10%2F3+%29%2At+
(1) +6+=+%28+5%2F3+%29%2At+
(1) +t+=+%283%2F5%29%2A6+
(1) +t+=+3.6+ hrs
OK