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Question 1161979: ok so I'm completely stumped, please help? Theres too many numbers here
3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
a) 8
b) 9
c) 10
d) 11
e) 12
Found 5 solutions by josgarithmetic, Edwin McCravy, math_helper, ikleyn, greenestamps:
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! One job is "empty a tank". Assume that each pump each works at the same rate.
n, how many pumps
r, rate for one pump
h, hours of work in a day
d, number of days
1, the job, taken as one whole job
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3 pumps, working 8 hours a day, can empty a tank in 2 days.
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Using RATE*TIME=JOBS
 --------------you do not really need to solve this for r, but you could if you wanted.
The time is actually in the unit of hours. This is as  , but you can use both variables for the formula, assigning values as you go.
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How many hours a day must 4 pumps work to empty the tank in 1 day?
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Simplify this.
Now you have this system of two equations in two unknown variables:
Simply divide the second equation by the first equation of this system; simplify and compute. h, number of hours now solved.
Answer by Edwin McCravy(20064)  (Show Source):
You can put this solution on YOUR website!
3 pumps, working 8 hours a day, can empty a tank in 2 days.
Double the pumps and half the days.
6 pumps, working 8 hours a day, can empty a tank in 1 day.
Double the pumps and half the hours per day.
12 pumps, working 4 hours a day, can empty a tank in 1 day.
Take 1/3 of the pumps, and triple the number of hours per day.
4 pumps, working 12 hours a day, can empty a tank in 1 day.
How many hours a day must 4 pumps work to empty the tank in 1 day?
Answer: 12 hours a day.
Edwin
Answer by math_helper(2461)  (Show Source):
You can put this solution on YOUR website!
Amount of time to empty the tank using 3 pumps: 16 hrs
The three pumps together pump out 1/16 of a tank per hour
Each pump does 1/3 of the work, therefore one pump empties
(1/3)*(1/16) = 1/48 of a tank per hour
We see now that one pump can empty the tank in 48 hours, so
4 pumps can empty it in (48/4) or 12 hours.
Answer by ikleyn(52881)  (Show Source):
You can put this solution on YOUR website! .
The entire job to empty the tank is 3 pumps * 8 hours per day * 2 days = 3*8*2 = 48 pump-hours.
Let x be the number of hours per day in the second scenario.
Then the equation for pump-hours is
48 = 4 pumps * x hours per day * 1 day,
or
48 = 4x.
which gives
x = 48/4 = 12 hours. ANSWER
Solved.
It is a standard, a simplest, a shortest and the most straightforward way to solve such problems.
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See the lesson
- Rate of work problems
in this site.
Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
Pay little attention to any response you get to any problem you post saying that a particular method is "standard" or "easiest". Different methods "work" better for different people; find one that works for you and use it.
This kind of problem is a good example of one for which there are many different equally good methods for solving.
Here is my preference for the method to solve this problem.
(1) Given: 3 pumps, 2 days --> 8 hours per day
(2) 4 pumps instead of 3 --> 3/4 as many hours per day
(3) 1 day instead of 2 --> twice as many hours per day
ANSWER: (8)(3/4)(2) = 12 hours per day
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