Question 1206761
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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.


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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 = <font color=red size=4>7 days</font> is the final answer.
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