SOLUTION: The speed of a stream is 5mph. If a boat travels 72 miles downstream in the same time that it takes to travel 36 miles upstream, what is the speed of the boat in still water?

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Question 734756: The speed of a stream is 5mph. If a boat travels 72 miles downstream in the same time that it takes to travel 36 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 the time for each of the 2 trips = +t+ hrs
Let the speed of the boat in still water = +s+
The boat's speed going downstream = +s+%2B+5+ mi/hr
The boat's speed going upstream = +s+-+5+ mi/hr
-------------
Equation for downstrteam trip:
(1) +72+=+%28+s+%2B+5+%29%2At+
Equation for upstrteam trip:
(2) +36+=+%28+s+-+5+%29%2At+
--------------------
(1) +72+=+s%2At+%2B+5t+
and
(2) +36+=+s%2At+-+5t+
-------------------
(2) +s%2At+=+36+%2B+5t++
Substitute (2) into (1)
(1) +72+=+36+%2B+5t+%2B+5t+
(1) +10t+=+36+
(1) +t+=+3.6+
and
(2) +36+=+%28+s+-+5+%29%2A3.6+
(2) +10+=+s+-+5+
(2) +s+=+15+
The speed of the boat in still water is 15 mi/hr
check:
(1) +72+=+s%2At+%2B+5t+
(1) +72+=+15t+%2B+5t+
(1) +72+=+20t+
(1) +t+=+3.6+
OK
(2) +36+=+s%2At+-+5t+
(2) +36+=+15t+-+5t+
(2) +36+=+10t+
(2) +t+=+3.6+
OK