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Question Number 95416 by john santu last updated on 25/May/20

$$\mathrm{It}\mathrm{takes}12\mathrm{hours}\mathrm{to}\mathrm{fill}\mathrm{a}\mathrm{swimming}$$$$\mathrm{pool}\mathrm{using}2\mathrm{pipes}.\mathrm{If}\mathrm{the}\mathrm{larger}$$$$\mathrm{pipe}\mathrm{used},\mathrm{for}4\mathrm{hours}\mathrm{and}\mathrm{the}$$$$\mathrm{small}\mathrm{pipe}\mathrm{for}9\mathrm{hours},\mathrm{only}\mathrm{half}$$$$\mathrm{the}\mathrm{pool}\mathrm{is}\mathrm{filled}.\mathrm{How}\mathrm{long}\mathrm{would}$$$$\mathrm{it}\mathrm{take}\mathrm{for}\mathrm{each}\mathrm{pipe}\mathrm{alone}\mathrm{to}$$$$\mathrm{fill}\mathrm{the}\mathrm{pool}?$$

Commented by PRITHWISH SEN 2 last updated on 25/May/20

$$\mathrm{x}\times \frac{4}{12}+(1-\mathrm{x})\times \frac{9}{12}=\frac{1}{2}$$$$\mathrm{x}=\frac{3}{5}$$$$\therefore \mathrm{the}\mathrm{bigger}\mathrm{pipe}=12\times \frac{5}{3}=20\mathrm{hrs}$$$$\mathrm{\&}\mathrm{the}\mathrm{smaller}\mathrm{pipe}=\frac{12}{(1-\frac{3}{5})}=30\mathrm{hrs}$$

Commented by john santu last updated on 25/May/20

$$\mathrm{yess}$$

Commented by pete last updated on 30/May/20

$$\mathrm{can}\mathrm{you}\mathrm{please}\mathrm{explain}\mathrm{your}\mathrm{reasonig}\mathrm{small},$$$$\mathrm{I}\mathrm{am}\mathrm{strugling}\mathrm{to}\mathrm{explain}\mathrm{it}\mathrm{to}\mathrm{my}\mathrm{son}.\mathrm{Please}$$

Commented by PRITHWISH SEN 2 last updated on 30/May/20

$$\mathrm{whose}?$$

Answered by mr W last updated on 25/May/20

$$\frac{12}{L}+\frac{12}{S}=1$$$$\frac{4}{L}+\frac{9}{S}=\frac{1}{2}$$$$\Rightarrow \frac{1}{L}=\frac{1}{20}\Rightarrow L=20h$$$$\Rightarrow \frac{1}{S}=\frac{1}{30}\Rightarrow S=30h$$$$largepipeneeds20h,smallpipe30h.$$

Commented by john santu last updated on 25/May/20

$$\mathrm{yess}$$

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