SOLUTION: Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed of her boat in still water is 9 km/hr. Find the speed of the stream. These word problems are tough, i appreci

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Question 170728This question is from textbook
: Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed of her boat in still water is 9 km/hr. Find the speed of the stream.
These word problems are tough, i appreciate any help! This question is from textbook

Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let s=speed of stream

Remember, the distance-rate-time formula is

d=rt


d%2Fr=t Divide both sides by r to solve for t.


t=d%2Fr Rearrange the equation.


So when she goes upstream (against the current), the stream is slowing her down. So this means that r=9-s and d=12. So the equation for the upstream portion of the journey is:

t=12%2F%289-s%29

When she goes downstream (with the current), the stream is speeding her up. So this means that r=9%2Bs and d=12. So the equation for the downstream portion of the journey is:

t=12%2F%289%2Bs%29


Now simply add these two equations together to get the total time 3 hours like this:


12%2F%289-s%29%2B12%2F%289%2Bs%29=3


12%289%2Bs%29%2B12%289-s%29=3%289-s%29%289%2Bs%29 Multiply both sides by the LCD %289-s%29%289%2Bs%29 to clear the fractions.


12%289%2Bs%29%2B12%289-s%29=3%2881-s%5E2%29 FOIL


108%2B12s%2B108-12s=243-3s%5E2 Distribute


216=243-3s%5E2 Combine like terms.


-27=-3s%5E2 Subtract 243 from both sides.


9=s%5E2 Divide both sides by -3.


s=3 Take the square root of both sides. Note: only the positive square root is considered.

So the speed of the stream is 3 km/hr

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed of her boat in still water is 9 km/hr. Find the speed of the stream.
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Call the speed of the stream w (for water).
Going upstream, her speed (with respect to the land) is 9-w
Going downstream, it's 9+w
See that?
The time it takes is the distance (s) over the speed.
So upstream it's 12/(9-w) hours
Downstream is 12/(9+w) hours
Make sense so far?
Now, 12/(9-w) + 12/(9+w) = 3
It's no longer a "word problem", it's one equation in one unknown.
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12/(9-w) + 12/(9+w) = 3
4/(9-w) + 4/(9+w) = 1
Multiply thru by (9-w)*(9+w)
4(9+w) + 4(9-w) = w^2 - 81
72 = w^2 - 81
w^2 = 9
w = 3 km/hr (also -3, but that makes no sense and can be discarded)