SOLUTION: Can you walk me through this probably simple word problem: If I had the total gallons then I could determine this easier, so I am stumped:
" The swimming pool can be filled in 1
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" The swimming pool can be filled in 1
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Question 257730: Can you walk me through this probably simple word problem: If I had the total gallons then I could determine this easier, so I am stumped:
" The swimming pool can be filled in 12 hours with a pipe or 30 hours using a hose. How long will it take if both are used?"
I want to say 21 hours but that would be too easy?? Found 3 solutions by ankor@dixie-net.com, richwmiller, jsmallt9:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The swimming pool can be filled in 12 hours with a pipe or 30 hours using a hose. How long will it take if both are used?"
:
Let t = time required using both
:
Let the completed job = 1 (a full pool)
:
Each device will do a fraction of the job, the two fractions add up to 1 + = 1
Multiply by a common multiple to get rid of the denominators, 60 will work, results
5t + 2t = 60
7t = 60
t =
t = 8.57 hrs working together
:
:
See if that's true, check on calc:
8.57/12 + 8.57/30 =
.714 + .286 = 1
You can put this solution on YOUR website! This is a typical work problem.
We have to find out how much work is done in one hour then add them
The two together has to be less than the faster alone but the slower doesn't contribute much.
In one hour the pipe can do 1/12 of the job.
The hose can do 1/30 of the job in an hour
j/12+j/30=1
lcd 60
5j/60+2j/60=7j/60
7j=60
j=60/7
j=8.57143 hours
about 8 hrs 34 minutes 17 seconds so the slower contributed 2.5 hours savings
You can put this solution on YOUR website! The key to these kinds of problems is to figure out how much of the total task can be done by each person/entity in one hour and then use these figures to solve the problem.
The pipe can do the entire task by itself in 12 hours. This means that the pipe can do 1/12 of the task in 1 hour.
The hose can do the entire task by itself in 30 hours. This means that the hose can do 1/30 of the task in 1 hour.
Working together the pipe and hose can do (1/12 + 1/30) of the task each hour.
Let x = the number of hours it takes both the pope and the hose to fill the pool. Then
Multiplying both sides by 60/7 we get:
(