You can
put this solution on YOUR website! PLEASE HELP! One pipe can fill a swimming pool in 5 hours less than another.
Together they fill the swimming pool in 5 hours. How long would it take each
pipe to fill the tank alone?
Make this chart:
D = deeds done = R = T =
No. of pools filled Rate in pools/hr Time in hours
Fast pipe
Slow pipe
Both together
Let the time for the slow pipe = x
The time for fast pipe is x-5
Fill in the times.
D = deeds done = R = T =
No. of pools filled Rate in pools/hr Time in hours
Fast pipe x-5
Slow pipe x
Both together 5
Now use the fact that in all three cases the number of pools filled is 1.
D = deeds done = R = T =
No. of pools filled Rate in pools/hr Time in hours
Fast pipe 1 x-5
Slow pipe 1 x
Both together 1 5
Now use R = D/T to fill in the rates
D = deeds done = R = T =
No. of pools filled Rate in pools/hr Time in hours
Fast pipe 1 1/(x-5) x-5
Slow pipe 1 1/x x
Both together 1 1/5 5
Now we form our equation from
Rate of fast pipe + Rate of slow pipe = Their combined rate
(That reasoning is similar to the fact that when a boat is traveling
downstream we add the rate of the boat to the rate of the river to
find their combined rate.)
1/(x-5) + 1/x = 1/5
Can you solve that? It requires the quadratic formula
_
Answers: x = (15 ± 5Ö5)/2 approximately = 13.09 hrs and 1.91 hrs. for the
time of the slow pipe.
We discard the 1.91 hours because that would give a negative number for the
hours it takes the fast pipe to fill the pool.
So the answers are, approximately: It takes the slow pipe 13.09 hours and
the fast pipe 5 hours less, or 8.09 hours.
Edwin
AnlytcPhil@aol.com
