At a chemical plant, a tank is filled with two liquids through tap A and tap B on top and emptied via valve at the bottom. Tap A on its own fills the tank in 15 minutes and tap B in 6 minutes. When opened, the valve can drain the tank in 30 minutes with both taps closed off. How long will the tank take to fill if the two taps and the valve are fully opened at the same time?
Answer: A nice, steady start to the month. Well done in order of correct-reply to: France Veillette, chef environnement, Usine de Joliette, Bridgestone Canada Inc., Canada: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; Vivian Zhou, senior business development & market intelligence analyst. BU RE PLT APAC, Continental Tires (Shanghai) Co. Ltd, Shanghai, China; Daniel Willrich, redakteur, AutoRäderReifen-Gummibereifung, Hannover, Germany; David Mann, key account manager, SPC Rubber Compounding, UK; Michele Girardi, Scame Mastaf Spa, Suisio, Italy; Paul Knutson, textile engineer, Timken Belts, Springfield, Missouri, USA; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria.
Answer: 5 minutes.
Just assume the tank has a capacity of 600 litres (for ease of mental arithmatic using common denominators).
Tap A fills the tank in 15 minutes so rate of entry is 600/15 = 40 litres/minute.
Tap B fills at a rate of 600/6 = 100 litres/minute. So the tank fills at a constant rate of 140 litres/minute with both taps fully open.
The valve empties in 30 minutes. This an average rate of 600/30 = 20 litres/minute.
The tank drains faster to start with, due to a higher pressure at the exit valve. The variable rate at which the tank empties whilst filling however is the exact reverse of the variable rate when the tank emptied.
The net filling rate is therefore still (40 + 100) - 20 = 120 litres/minute, so the tank fills in exactly 600/120 = 5 minutes.
The tank however is more than half full after 2 1/2 minutes!
it takes 5 minutes to fill the tank. Each minute 1/15 of the tank is filled by tap A plus 1/6 of the tank is filled by B, while 1/30 of the tank is emptied through the valve. This means 7/30 is going in with 1/30 going out, which is why 6/30 or 1/5 of the tank is filled per minute.
First, we need to know the flow of each tap and valve
Flow = F Volume = V Time = t
Flow is given by F = V/t; from this, t = V/F
In the other side: Total flow = flow tap 1 + flow tap2 – flow drain valve
As volume is constant, we have
Total flow = F = V/t1 + V/t2 – V/t3
F = V/15 + V/6 – V/30
Solving t = V/F we have: t = V/V(1/15+1/6-1/30)
Cancelling V; we have: t = 1/(1/15+1/6+1/30) = 5
Very well done to France Veillette and Stephan Paischer who were spot on with 1911. Special mentions also to Andrew Knox 1912-13, and not too far out: Paul Knutson,1905; and David Mann, 1901. The article was actually published in an issue dated 4 Nov 1911.
Try to guess the year-of-publication of the following snippet from the ERJ archives, which date back to 1884.