August 29th, 2014, 09:13 AM  #1 
Member Joined: Aug 2014 From: scotland Posts: 45 Thanks: 0  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? 
August 29th, 2014, 04:23 PM  #2 
Senior Member Joined: Aug 2008 From: Blacksburg VA USA Posts: 338 Thanks: 4 Math Focus: primes of course  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*(Tf0)=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 04:24 PM. Reason: typo 

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