SOLUTION: The currents speed Is 3 mph. Sean kayaks 4mi upstream the same time it takes him 10 mi to go downstream. What's the speed of the kayak in still water????

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Question 412453: The currents speed Is 3 mph. Sean kayaks 4mi upstream the same time it takes him 10 mi to go downstream. What's the speed of the kayak in still water????
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
3 mi/hr is the speed of current
Let s = speed of kayak in still water
going downstream:
speed = s+%2B+3
going upstream:
speed = s+-3
------------------
given:
(1) 4+=+%28s+-+3%29%2At%0D%0Aand%0D%0A%282%29+%7B%7B%7B10+=+%28s+%2B+3%29%2At
-----------------
This is 2 equation and 2 unknowns, so it's solvable
(1) 4+=+%28s+-+3%29%2At%0D%0A%0D%0A%281%29+%7B%7B%7B4+=+s%2At+-+3t
(2) 10+=+s%2At+%2B+3t
Subtract (1) from (2)
(2) 10+=+s%2At+%2B+3t
(1) -4+=+-s%2At+%2B+3t
6+=+6t
t+=+1 hr
Now I plug this into (1) and solve for s
(1) 4+=+s%2A1+-+3%2A1
(1) 4+=+s+-+3
(1) s+=+7
The speed of the kayak in still water is 7 mi/hr
check answer:
(2) 10+=+%28s+%2B+3%29%2At
(2) 10+=+%287+%2B+3%29%2A1
10+=+10
OK