SOLUTION: If 18 pumps can raise 2170 tonnes of water in 10 days, working 7 hours a day; in how many days will 16 pumps raise 1736 tonnes of water, working 9 hours a day?

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Question 1206761: If 18 pumps can raise 2170 tonnes of water in 10 days, working 7 hours a day; in how many days will 16 pumps raise 1736 tonnes of water, working 9 hours a day?
Found 4 solutions by ikleyn, MathLover1, greenestamps, math_tutor2020:
Answer by ikleyn(52756)   (Show Source): You can put this solution on YOUR website!
.
If 18 pumps can raise 2170 tons of water in 10 days, working 7 hours a day;
in how many days will 16 pumps raise 1736 tons of water, working 9 hours a day?
~~~~~~~~~~~~~~~~~~~~ 

Raising 2170 tons of water requires  18*10*7 = 1260 pump-hours.


So, the rate is   =   tons of water per one pump-hour.


To raise 1736 tons of water, using 16 pumps working 9 hours a day,

     =  = 7 days is needed.

Solved.

----------------

To see many other similar  (and different)  problems,  solved by the same method,  look into the lesson
    - Rate of work problems
in this site.

It was written specially for you,  to make your horizon  WIDER.



Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

let the number of days be






days


Answer by greenestamps(13195)   (Show Source): You can put this solution on YOUR website!


Both of the responses from other tutors show basically the same good method for solving the problem.

Here is a different method for working problems like this that I personally like.

We are given that it takes 10 days for a certain given amount of work to get done, and we are asked how many days it would take with different parameters. We can find the answer by multiplying the given figure of 10 days by ratios representing the change in each parameter.

(1) 16 pumps instead of 18; fewer pumps means more time; multiply by 18/16 = 9/8.
(2) 1736 tonnes of water instead of 2170; fewer tonnes means less time; multiply by 1736/2170 = 4/5.
(3) working 9 hours a day instead of 7; more hours per day means fewer days; multiply by 7/9.



ANSWER: 7 days
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

This method may be a bit longer but it's another approach to think about.

(7 hours per day)*(10 days) = 70 hours

18 pumps can raise 2170 tonnes of water in 70 hours.

Divide the work equally among the 18 pumps. This assumes all pumps have the same capability.
2170/18 = 120.555555555556
This is the approximate amount of water each pump will handle.
The 5s go on forever but we have to round at some point.

rate*time = amountDone
rate*(70 hours) = 120.555555555556 tonnes of water
rate = 120.555555555556/70
rate = 1.722222222222 tonnes per hour

Notice:
31/18 = 1.722222222222
which matches up with the fraction that tutor ikleyn got.

--------------------------------------------------------------------------

1 pump works at a rate of roughly 1.722222222222 tonnes per hour.
16 pumps work at a combined rate of 16*1.722222222222 = 27.555555555552 tonnes per hour.

rate*time = amountDone
(27.555555555552 tonnes per hr)*time = 1736
time = 1736/27.555555555552
time = 63.000000000008 hours

There's some rounding error. But if you used the exact fraction forms, then you'll land on 63 exactly.
The more precision you have in your scratch work, the more confident you can be in what the exact answer is.
I suppose it would also depend on your calculator's displayed precision.

x = number of days
The 16 pumps work 9 hour days, so 9x is the total number of hours
9x = 63
x = 63/9
x = 7 days is the final answer.
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