SOLUTION: It took a crew 8 h 32 min to row 8 km upstream and back again. If the rate of flow of the stream was 7 km/h, what was the rowing speed of the crew in still water?

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Question 1034987: It took a crew 8 h 32 min to row 8 km upstream and back again. If the rate of flow of the stream was 7 km/h, what was the rowing speed of the crew in still water?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
It took a crew 8 h 32 min to row 8 km upstream and back again.
If the rate of flow of the stream was 7 km/h, what was the rowing speed of the crew in still water?
:
Let s = rowing speed in still water.
then
(s-7) = effective speed upstream
and
(s+7) = effective speed downstream
:
Change 8 hrs 32 min to hrs: 8 + 32/60 = 8 + 8/15 hrs = 128/15
:
write a time equation, time = dist/speed
Time up + time down = 8hr 32 min
8%2F%28%28s-7%29%29 + 8%2F%28%28s%2B7%29%29 = 128%2F15
simplify, divide by 8
1%2F%28%28s-7%29%29 + 1%2F%28%28s%2B7%29%29 = 16%2F15
multiply by 15(s-7)(s+7), cancel the denominators
15(s+7) + 15(s-7) = (s-7)(s+7)*16
15s + 105 + 15s - 105 = 16(s^2 - 49)
30s = 16s^2 - 784
0 = 16s^2 - 30s - 784
simplify, divide by 2
8s^2 - 15s - 392 = 0
you can use the quadratic formula, but this will factor to
(8s+49)(s-8) = 0
the positive solution is all we want here
s = 8 km/hr in still water
:
:
See if that checks out. Find the actual time each way
8/(8-7) = 8 hrs upstream
8/(8+7) = .533 hrs which is 32 min down stream