SOLUTION: A boat goes 210 miles downstream in the same time it can go 180 miles upstream the speed of the current is 4mph find the speed of the boat in still water

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Question 1092529: A boat goes 210 miles downstream in the same time it can go 180 miles upstream the speed of the current is 4mph 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 +s+ = the speed of the boat in still water
Let +t+ = time in hrs to go either
downstream or upstream
-----------------
Equation for going downstream:
(1) +210+=+%28+s+%2B+4+%29%2At+
Equation for going upstream:
(2) +180+=+%28+s+-+4+%29%2At+
--------------------------------
(1) +t+=+210+%2F+%28+s+%2B+4+%29+
Plug (1) into (2)
(2) +180+=+%28+s+-+4+%29%2A210+%2F+%28+s+%2B+4+%29+
(2) +180%2A%28+s+%2B+4+%29+=+210%2A%28+s+-+4+%29+
(2) +180s+%2B+720+=+210s+-+840+
(2) +30s+=+1560+
(2) +s+=+52+
The speed in still water is 52 mi/hr
----------------------------------
check:
(1) +t+=+210+%2F+%28+52+%2B+4+%29+
(1) +t+=+210+%2F+56+
(1) +t+=+3.75+ hrs
and
(2) +t+=+180+%2F+%28+52+-+4+%29+
(2) +t+=+180+%2F+48+
(2) +t+=+3.75+ hrs
OK