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Question 671640: Wanda paddles six miles downstream in 1 hour and her friend minnie rowing 1 mph faster goes upstream 6 miles in 2 hours. Find the speed of the current and the girls speeds
I tried b-c=3mph
b+c=6mph and tried to solve out from there but the extra mile per hour is throwing me off
Any help greatly appreciated.
thanks
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! You need to set up the appropriate algebraic equations - not just try a few numbers etc.
Let W = Wanda's speed
Let S = the stream's speed
Let F = Friend's speed
Now what do we know?
(1) W + S = 6, as Wanda goes 6mi in 1 hr downstream (with the current, so add)
(2) F - S = 3, as her friend goes 6mi in 2hr (6hr/2hr = 3mph) upstream (so subtract) and
(3) F = W +1, because we are told that Wanda's friend paddles 1 mph faster than Wanda.
Now for the algebra. If we add equation (1) to equation (2) we get
(4) W + S + F - S = 6 + 3 or
(5) W + F = 9, OK so far?
Now substitute F of (3) into (5) and get
(6) W + (W + 1) = 9 or
(7) 2*W = 8 or
(8) W = 4
Using (8) in (3) we have
(9) F = 4 + 1 or
(10) F = 5
Using (1) we get
(11) W + S = 6 or
(12) 4 + S = 6 or
(13) S = 2
Let's check these values using (2).
Is (F - S = 3)?
Is (5 - 2 = 3)?
Is (3 = 3)? Yes
Answer: Wanda paddles at 4 mph and her friend paddles at 5 mph and the stream is moving at 2 mph.
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