Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 150894: 4. 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.: 4. 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.
Answer by jim_thompson5910(8292) 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/r=t Divide both sides by r to solve for t.


t=d/r 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/(9-s)

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

t=12/(9+s)


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


12/(9-s)+12/(9+s)=3


12(9+s)+12(9-s)=3(9-s)(9+s) Multiply both sides by the LCD (9-s)(9+s) to clear the fractions.


12(9+s)+12(9-s)=3(81-s^2) FOIL


108+12s+108-12s=243-3s^2 Distribute


216=243-3s^2 Combine like terms.


-27=-3s^2 Subtract 243 from both sides.


9=s^2 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