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August 29th, 2014, 08:13 AM   #1
Joined: Aug 2014
From: scotland

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Filling a tank

Water fill a tank at a rate of 150litres during first hour, 350 in the second hour, 550 in the third hour and so on.
Find the time taking to fill tank 16mx9mx9m

I know the volume is 1296m^3
and the volume in litres is 1296 x 1000
= 1296000.
But is there a forumlae to link the +200 in L/h to work it out easier?
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August 29th, 2014, 03:23 PM   #2
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From: Blacksburg VA USA

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tank filling

It is similar to a speed -distance problem.
Recall derivatives are "rates", and antiderivatives/integration returns to the original "thing", in this case volume.
Do you see how this can help you solve it?

If I had a constant speed of 100 mph (initial d=0), how long to go 500 miles?
Let the final time be Tf, start time be Ts (here 0)
$\displaystyle integral(100) from Ts to Tf $yields
$\displaystyle 100(Tf)-100(0) + K$
we know K=0 since initial d=0. K is the constant of integration
100*(Tf-0)=500 gives Tf=5 hours. So one has gone 500 miles in 5 hours.

Your problem is only slightly different ...
rather than a constant rate, yours is of the form rate=A*B(t) (it changes with time)

Can you tell us what you think A and B(t) are?

Last edited by billymac00; August 29th, 2014 at 03:24 PM. Reason: typo
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