SOLUTION: The Speed of a river is 7mph. If a boat travels 20 miles downstream in the same time it takes to travel 10 miles upstream, find the speed of the boat in still water?

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Question 804041: The Speed of a river is 7mph. If a boat travels 20 miles downstream in the same time it takes to travel 10 miles upstream, find 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 +t+ = the time in hours going both
upstream and downstream
Let +s+ = the speed of the boat in still water
-----------------
Going downstream:
(1) +20+=+%28+s+%2B+7+%29%2At+
Going upstream:
(2) +10+=+%28+s+-+7+%29%2At+
--------------------
(1) +20+=+s%2At+%2B+7t+
and
(2) +10+=+s%2At+-+7t+
-------------------
Subtract (2) from (1)
(1) +20+=+s%2At+%2B+7t+
(2) +-10+=+-s%2At+%2B+7t+
+10+=+14t+
+t+=+5%2F7+
-----------
(1) +20+=+%28+s+%2B+7+%29%2At+
(1) +20+=+%28+s+%2B+7+%29%2A%285%2F7%29+
(1) +140+=+5s+%2B+35+
(1) +5s+=+105+
(1) +s+=+21+
The speed of the boat in still water is 21 mi/hr
check:
(2) +10+=+%28+s+-+7+%29%2At+
(2) +10+=+%28+21+-+7+%29%2A%285%2F7%29+
(2) +10+=+14%2A%285%2F7%29+
(2) +70+=+70+
OK