SOLUTION: It took a crew 2.75 hours to row 6 km upstream and back again (6 km one way ). If the rate of flow of the stream was 3 km/hr, what would be the rowing speed of the crew in still wa
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Question 941339: It took a crew 2.75 hours to row 6 km upstream and back again (6 km one way ). If the rate of flow of the stream was 3 km/hr, what would be the rowing speed of the crew in still water ? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! It took a crew 2.75 hours to row 6 km upstream and back again (6 km one way
If the rate of flow of the stream was 3 km/hr, what would be the rowing speed of the crew in still water?
:
Let s = their speed in still water
then
(s+3) = effective speed downstream
and
(s-3) = effective speed upstream
:
Write time equation; time = dist/speed
:
time upstr + time downstr = 2.75 hrs + = 2.75
:
multiply equation by (s-3)(s+3)
(s+3)(s-3)* + (s+3)(s-3)* = 2.75(s+3)(s-3)
:
Cancel the denominator, FOIL the right side
6(s-3) + 6(s+3) = 2.75(s^2-3s+3s-9)
:
distribute. combine like terms
6s - 18 + 6s + 18 = 2.75(s^2-9)
12s = 2.75s^2 - 24.75
:
A Quadratic equation
0 = 2.75s^2 - 12s - 24.75
:
Use the quadratic formula, a=2.75; b=-12; c=-24.75
I got a positive solution of:
s = 5.89 km in still water
:
;
Confirm this; find the actual time each way
6/2.89 = 2.08 hrs upstream (3 km/hr slower)
6/8.89 = 0.67 hrs downstream (3 km/hr faster)
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total: 2.75 hrs
:
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