SOLUTION: A motorboat travels 756 mi in 9 hours going upstream and 684 mi in 6 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Question 767511: A motorboat travels 756 mi in 9 hours going upstream and 684 mi in 6 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Found 2 solutions by stanbon, lwsshak3:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A motorboat travels 756 mi in 9 hours going upstream and 684 mi in 6 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
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Upstream DATA:
distance = 756 miles ; time = 9 hrs ; rate = 756/9 = 84 mph
------
Downstream DATA:
distance = 684 miles ; time = 6 hrs ; rate = 684/6 = 114 mph
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Equations:
b - c = 84
b + c = 114
------
2b = 198
b = 99 mph (speed of the boat in still water)
------
Solve for "c":
b +c = 114
99 + c = 114
c = 15 mph (speed of the current)
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Cheers,
Stan H.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
A motorboat travels 756 mi in 9 hours going upstream and 684 mi in 6 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
***
let x=rate of speed of motorboat in still water
let c=rate of speed of current
x+c=rate of speed of motorboat downstream
x-c=rate of speed of motorboat upstream
travel time=distance/rate of speed
...
756/(x-c)=9
684/(x+c)=6
..
9x-9c=756
6x+6c=684
..
54x-54c=4536
54x+54c=6156
add
108x=10692
x=99
6c=684-6x=684-594=90
c=15
rate of speed of motorboat in still water=99 mph
rate of speed of current=15 mph

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