SOLUTION: A barge travels along a river between Metro City and Smithport which are 50 miles away from each other. The speed of the current is 1.7 miles per hour. If the barge can make the do

Question 939391: A barge travels along a river between Metro City and Smithport which are 50 miles away from each other. The speed of the current is 1.7 miles per hour. If the barge can make the downstream trip in 6.5 hours less than it can travel the upstream trip, then what is the barge's speed in still water?
My professor said the answer is 5.4 mph, but no matter what I try, I can't seem to come up with that answer. Thank you!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A barge travels along a river between Metro City and Smithport which are 50 miles away from each other. The speed of the current is 1.7 miles per hour. If the barge can make the downstream trip in 6.5 hours less than it can travel the upstream trip, then what is the barge's speed in still water?
***
let x=speed of barge in still water
x+1.7=speed of barge downstream
x-1.7=speed of barge upstream
travel time=distance/speed
..

lcd:(x-1.7)(x+1.7)
50(x+1.7)-50(x-1.7)=6.5(x-1.7)(x+1.7)
50x+85-50x+85=6.5(x^2-1.7^2)=6.5(x^2-2.89)=6.5x^2-18.785
170=6.5x^2-18.785
6.5x^2=188.785
x^2=188.785/6.5=29.04
x=√29.04=5.4 (rounded)
speed of barge in still water≈5.4 mph
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