SOLUTION: Joe can row a boat a distance of 12.75 miles in 1.5 hours when he is rowing with the current. It takes him 1.7 hours to row the same distance when he is rowing against the current

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Question 654723: Joe can row a boat a distance of 12.75 miles in 1.5 hours when he is rowing with the current. It takes him 1.7 hours to row the same distance when he is rowing against the current. What is the rate of the current? At what rate can Joe row in still water?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Joe can row a boat a distance of 12.75 miles in 1.5 hours when he is rowing with the current. It takes him 1.7 hours to row the same distance when he is rowing against the current. What is the rate of the current? At what rate can Joe row in still water?
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let x=Joe's rowing rate in still water
let c=rate of current
x+c=rate with the current
x-c= rate against the current
distance/travel time=rate
..
12.75/1.5=x+c
12.75/1.7=x-c
..
1.5x+1.5c=12.75
1.7x+1.7c=12.75
..
multiply first equation by 1.7 and second equation by 1.5
2.55x+2.55c=21.675
2.55x-2.55c=19.125
add
5.10x=40.8
x=8
1.5c=12.75-1.5x=12.75-12=.75
c=.75/1.5=.5
..
Joe's rowing rate in still water=8 mph
rate of current=0.5 mph