SOLUTION: Bill wants to fill his pool up. A fire hose sprays 13.5 times per minute faster than a garden hose. If the fire hose and garden hose combined fill the pool in 107 minutes, how long

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Bill wants to fill his pool up. A fire hose sprays 13.5 times per minute faster than a garden hose. If the fire hose and garden hose combined fill the pool in 107 minutes, how long      Log On


   

Question 1006200: Bill wants to fill his pool up. A fire hose sprays 13.5 times per minute faster than a garden hose. If the fire hose and garden hose combined fill the pool in 107 minutes, how long would it take for the garden hose alone to fill the pool?
13.5x + x = 107
X=107/14.5
But I know this is incorrect and I cannot seem to figure it out.
Found 4 solutions by josgarithmetic, Boreal, josmiceli, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Use rate unit as POOL per MINUTES. 

                RATE

Garden Hose      1%2F%2813.5x%29

Fire Hose        1%2Fx

BOTH             1%2F107


To try to make the two separate rates relationship clearer, try to compare their rates and see how the comparison agrees with the description.

When that is understood, solve for x, in 1%2F%2813.5x%29%2B1%2Fx=1%2F107.

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
garden hose takes x minutes
fire hose takes x/13.5 minutes, that is 13.5 times faster. Now set the two equal to 107 minutes.
107=x+x/13.5 minutes
multiply both sides by 13.5
1444.5=13.5x+x=14.5x
x=1444.5/14.5
=99.6 minutes for the garden hose
99.6/13.5=7.4 minutes for the fire hose.
The issue here is that the firehose is 13.5 times faster, and it takes x/13.5 minutes to fill it.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rate of filling with either the
fire hose or garden hose is expressed as:
[ fraction of pool filled ] / [ time to fill that fraction of pool ]
So, I will say:
+r%5B1%5D+ = rate of filling for garden hose
+r%5B2%5D+ = rate of filling for fire hose
----------------------------------
I can also say:
+r%5B2%5D+=+13.5r%5B1%5D+
also given:
+r%5B1%5D+%2B+r%5B2%5D+=+1%2F107+
which is [ 1 pool filled ] / [ 107 minutes ]
---------------------------------
By substitution:
+r%5B1%5D+%2B+13.5r%5B1%5D+=+1%2F107+
+14.5r%5B1%5D+=+1%2F107+
+r%5B1%5D+=+1%2F1551.5+
and
+r%5B2%5D+=+13.5r%5B1%5D+
+r%5B2%5D+=+13.5%2A%28+1%2F1551.5+%29+
+r%5B2%5D+=+1%2F114.93+
-------------------------
For the garden hose:
+1551.5%2F60+=+25.858+
+.858%2A60+=+51.5+
It will take 25 hrs 51.5 minutes
to fill the pool
--------------------------
check:
+r%5B1%5D+%2B+r%5B2%5D+=+1%2F107+
+1%2F1551.5+%2B+1%2F114.93+=+1%2F107+
+.0006445+%2B+.0087+=+.009346+
+.0093445+=+.009346+
Looks close enough. These are pretty strange
numbers. I would definitely get another
opinion on this. Hopefully, I got it

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Bill wants to fill his pool up. A fire hose sprays 13.5 times per minute faster than a garden hose. If the fire hose and garden hose combined fill the pool in 107 minutes, how long would it take for the garden hose alone to fill the pool?
13.5x + x = 107
X=107/14.5
But I know this is incorrect and I cannot seem to figure it out.
Garden hose takes 13.5 TIMES AS LONG as the fire hose, not 13.5 times longer.

Thus, garden hose takes: highlight_green%281551.5%29 minutes