Select the correct answerA chemical plant has four tanks (A, B, C and D), each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows:From A to B at 20 litres/minuteFrom C to A at 90 litres/minuteFrom A to D at 10 litres/minuteFrom C to D at 50 litres/minuteFrom B to C at 100 litres/minuteFrom D to B at 110 litres/minuteWhich tank gets emptied first and how long does it take to get emptied after pumping starts?radio_button_uncheckedC, 16.66 minradio_button_uncheckedC, 22 minradio_button_uncheckedD, 20 minradio_button_uncheckedD, 25 min
Question
Select the correct answerA chemical plant has four tanks (A, B, C and D), each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows:From A to B at 20 litres/minuteFrom C to A at 90 litres/minuteFrom A to D at 10 litres/minuteFrom C to D at 50 litres/minuteFrom B to C at 100 litres/minuteFrom D to B at 110 litres/minuteWhich tank gets emptied first and how long does it take to get emptied after pumping starts?radio_button_uncheckedC, 16.66 minradio_button_uncheckedC, 22 minradio_button_uncheckedD, 20 minradio_button_uncheckedD, 25 min
Solution
To find out which tank gets emptied first, we need to calculate the net flow of the chemical in or out of each tank per minute.
For tank A: Flow in from C = 90 litres/minute Flow out to B = 20 litres/minute Flow out to D = 10 litres/minute Net flow for A = Flow in - Flow out = 90 - (20 + 10) = 60 litres/minute (inflow)
For tank B: Flow in from A = 20 litres/minute Flow in from D = 110 litres/minute Flow out to C = 100 litres/minute Net flow for B = Flow in - Flow out = (20 + 110) - 100 = 30 litres/minute (inflow)
For tank C: Flow in from B = 100 litres/minute Flow out to A = 90 litres/minute Flow out to D = 50 litres/minute Net flow for C = Flow in - Flow out = 100 - (90 + 50) = -40 litres/minute (outflow)
For tank D: Flow in from A = 10 litres/minute Flow in from C = 50 litres/minute Flow out to B = 110 litres/minute Net flow for D = Flow in - Flow out = (10 + 50) - 110 = -50 litres/minute (outflow)
From the above calculations, we can see that tanks C and D are losing chemical, but D is losing at a faster rate. Therefore, tank D will be emptied first.
To find out how long it takes for tank D to be emptied, we divide the initial volume of the tank by the absolute value of the net flow rate:
Time = Volume / Flow rate = 1000 litres / 50 litres/minute = 20 minutes
So, the correct answer is "D, 20 min".
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