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Question Number 75896 by gugum last updated on 20/Dec/19

One pipe can fill a tank in 40 minutes  and an outlet pipe can empty the full  tank in 24 minutes. If both the pipes  are opened simultaneously, what time  will it take for the full tank to be  emptied?

$$\mathrm{One}\:\mathrm{pipe}\:\mathrm{can}\:\mathrm{fill}\:\mathrm{a}\:\mathrm{tank}\:\mathrm{in}\:\mathrm{40}\:\mathrm{minutes} \\ $$$$\mathrm{and}\:\mathrm{an}\:\mathrm{outlet}\:\mathrm{pipe}\:\mathrm{can}\:\mathrm{empty}\:\mathrm{the}\:\mathrm{full} \\ $$$$\mathrm{tank}\:\mathrm{in}\:\mathrm{24}\:\mathrm{minutes}.\:\mathrm{If}\:\mathrm{both}\:\mathrm{the}\:\mathrm{pipes} \\ $$$$\mathrm{are}\:\mathrm{opened}\:\mathrm{simultaneously},\:\mathrm{what}\:\mathrm{time} \\ $$$$\mathrm{will}\:\mathrm{it}\:\mathrm{take}\:\mathrm{for}\:\mathrm{the}\:\mathrm{full}\:\mathrm{tank}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{emptied}? \\ $$

Answered by mr W last updated on 20/Dec/19

pipe to fill: (1/(40))  pipe to empty: (1/(24))  both pipes (to empty): (1/(24))−(1/(40))  time: (1/((1/(24))−(1/(40))))=((40×24)/(40−24))=60 minutes

$${pipe}\:{to}\:{fill}:\:\frac{\mathrm{1}}{\mathrm{40}} \\ $$$${pipe}\:{to}\:{empty}:\:\frac{\mathrm{1}}{\mathrm{24}} \\ $$$${both}\:{pipes}\:\left({to}\:{empty}\right):\:\frac{\mathrm{1}}{\mathrm{24}}−\frac{\mathrm{1}}{\mathrm{40}} \\ $$$${time}:\:\frac{\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{24}}−\frac{\mathrm{1}}{\mathrm{40}}}=\frac{\mathrm{40}×\mathrm{24}}{\mathrm{40}−\mathrm{24}}=\mathrm{60}\:{minutes} \\ $$

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