SOLUTION: David rowed a boat upstream for three miles and then returned to point he started from. The entire journey took four hours. The speed of the stream is one mile per hour. Find David
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Question 1007220: David rowed a boat upstream for three miles and then returned to point he started from. The entire journey took four hours. The speed of the stream is one mile per hour. Find David's speed in still water.
David's speed in still water is
miles per hour. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! David rowed a boat upstream for three miles and then returned to point he started from.
The entire journey took four hours.
The speed of the stream is one mile per hour.
Find David's speed in still water.
:
let s = his speed in still water
then
(s-1) = effective speed upstream
and
(s+1) = effective speed downstream
:
Write time equation; time = dist/speed
:
time up + time down = 4 hrs + = 4
multiply equation by (s-1)(s+1), cancel the denominators and you ave
3(s+1) + 3(s-1) = 4s(s-1)(s+1)
3s + 3 + 3s - 3 = 4(s^2 - 1)
6s = 4s^2 - 4
Combine to form a quadratic on the right
0 = 4s^2 - 6s - 4
Simplify, divide by 2
2s^2 - 3s - 2 = 0
Factors to
(2s+1)(s-2) = 0
The positive solution
s = 2 mph in still water
:
:
Confirm this by finding the actual time each way, using the effective speeds
3/1 = 3
3/3 = 1
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total 4 hrs
