A and B are two pipes connected to a tank. A is the filler pipe and B is the ejector. The capacity of the tank is 6000L.The ejector pipe can eject water at the rate 4L/min higher than the filler pipe. The filler pipe can fill the tank 5 min later than the ejector pipe can eject. Find the flow rate of the ejector pipe in L/min(approx.).
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Step-by-step explanation:
Given : ejector pipe can eject water at the rate 4L/min higher than the filler pipe . The filler pipe can fill the tank 5 min later than the ejector pipe can eject
To find : flow rate of the ejector pipe in L/min(approx.).
solution:-
ejector pipe flow rate = E L/Min
Filler Pipe flow rate = E - 4 L/Min
Capacity of Tank = 6000 L
Time Taken by Ejector pipe = 6000/E Min
Time Taken by filler pipe = 6000/(E - 4) Min
The filler pipe can fill the tank 5 min later than the ejector pipe can eject.
=> 6000/(E - 4) = 6000/E + 5
=> 6000E = 6000(E - 4) + 5E(E - 4)
=> 6000E = 6000E - 24000 + 5(E² - 4E)
=> 5(E² - 4E) - 24000 = 0
=> E² - 4E - 4800 = 0
=> E = (4 ± √(4² - 4*(-4800)) ) /2
=> E = 2 + √4801 ( ignoring - ve value)
=> E = 2 + 69.3
=> E = 71.3
flow rate of the ejector pipe = 71.3 L/min
I hope it will help you to understand ❤
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