SOLUTION: 16 hours to fill a pool using a small hose a large hose connected to a different water supply can fill the same pool in just 12 hours the owner starts to fill the pool with the sma

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Question 1126597: 16 hours to fill a pool using a small hose a large hose connected to a different water supply can fill the same pool in just 12 hours the owner starts to fill the pool with the small hose at 8:00 am both hoses run together from 10:00 am to 3:00 pm what percentage of the pool is filled by 3:00 pm
Found 4 solutions by josmiceli, ikleyn, josgarithmetic, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
From 8 AM to 10 AM is 2 hrs
small hose rate of filling is:
[ 1 pool ] / [ 16 hrs ]
+%281%2F16%29%2A2+=+1%2F8+ of the pool gets filled
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From 10 AM to 3 PM is 5 hrs
+7%2F8+ of the pool is left to fill
Add the rates of the 2 hoses
+1%2F16+%2B+1%2F12+=+x%2F5+
Multiply both sides by +240+
+15+%2B+20+=+48x+
+48x+=+35+
+x+=+35%2F48+
This is +%2835%2F48%29%2A%287%2F8%29+=+245%2F384+
Note that +1%2F8+=+48%2F384+
So, the fraction that is filled is:
+245%2F384+%2B+48%2F384+=+293%2F384+
+293%2F384+=+.763+
76.3% of the pool is filled
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Definitely get a 2nd opinion & check math

Answer by ikleyn(52806) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The solution by  @josmicely  is incorrect.


            The solution by @josgaritmetic is  T O T A L L Y   I N C O R R E C T.


            For your safety, simply ignore it !


            The correct solution is below. 


The smaller hose worked 7 hours and filled  7%2F16 of the tank volume.


The larger hose worked 5 hours and filled  5%2F12 of the tank volume.


The part of the tank volume filled at 3:00 pm was


    7%2F16 + 5%2F12 = %287%2A9+%2B+5%2A12%29%2F144 = 123%2F144 = 41%2F48 = 85.42%  (approximately).


Answer.  At 3:00 pm,  the tank was filled at  41%2F48 = 85.42% of its volume (approximately).



Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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16 hours to fill a pool using a small hose a large hose connected to a different water supply can fill the same pool in just 12 hours the owner starts to fill the pool with the small hose at 8:00 am both hoses run together from 10:00 am to 3:00 pm what percentage of the pool is filled by 3:00 pm
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More Clearly Formatted
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16 hours to fill a pool using a small hose;
large hose connected to a different water supply can fill the same pool in just 12 hours;
The owner starts to fill the pool with the small hose at 8:00 am.
Both hoses run together from 10:00 am to 3:00 pm.
What percentage of the pool is filled by 3:00 pm?
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HOSE             RATES in POOL per HOURS

SMALL             1%2F16

LARGE             1%2F12

COMBINED       1%2F16%2B1%2F12=cross%287%2F144%29------MISTAKE


R, rate
T, time
V, amount of pool volume
RT=V 
time period     time quantity, hours       which hose      fill rate       fraction of pool vol

 8am-10am                  2                small            1%2F16         %281%2F16%29%2A2=1%2F8

10am-3pm                   5                combined         cross%287%2F144%29        cross%28%287%2F144%29%2A5=35%2F144%29




------------------------------------------------------------
----------EVERYTHING BELOW IS WRONG BECAUSE OF MISTAKE-----
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Total fraction of pool filled:
1%2F8%2B35%2F144
%281%2F8%29%2818%2F18%29%2B35%2F144
%2818%2B35%29%2F144
cross%2853%2F144%29, as fraction of the pool


Percent of Pool:
%28cross%2853%2F144%29%2A100%29
approximatelycross%2836.8%29highlight%28percent%29

Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!

16 hours to fill a pool using a small hose a large hose connected to a different water supply can fill the same pool in just 12 hours the owner starts to fill the pool with the small hose at 8:00 am both hoses run together from 10:00 am to 3:00 pm what percentage of the pool is filled by 3:00 pm
The smaller ran for 7 (8:00 a.m. - 3:00 p.m.) hours, while the larger ran for 5 (10:00 a.m. - 3:00 p.m.) hours. 

We then get: 

IGNORE all other wrong answers.