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

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

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

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

x×(4/(12))+(1−x)×(9/(12))= (1/2) x=(3/5) ∴ the bigger pipe = 12×(5/3) = 20 hrs & the smaller pipe = ((12)/((1−(3/5))))= 30 hrs

$$\mathrm{x}×\frac{\mathrm{4}}{\mathrm{12}}+\left(\mathrm{1}−\mathrm{x}\right)×\frac{\mathrm{9}}{\mathrm{12}}=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{x}=\frac{\mathrm{3}}{\mathrm{5}} \\ $$$$\therefore\:\mathrm{the}\:\mathrm{bigger}\:\mathrm{pipe}\:=\:\mathrm{12}×\frac{\mathrm{5}}{\mathrm{3}}\:=\:\mathrm{20}\:\mathrm{hrs} \\ $$$$\&\:\mathrm{the}\:\mathrm{smaller}\:\mathrm{pipe}\:=\:\frac{\mathrm{12}}{\left(\mathrm{1}−\frac{\mathrm{3}}{\mathrm{5}}\right)}=\:\mathrm{30}\:\mathrm{hrs} \\ $$

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

yess

$$\mathrm{yess} \\ $$

Commented by pete last updated on 30/May/20

can you please explain your reasonig small, I am strugling to explain it to my son. Please

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

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

whose ?

$$\mathrm{whose}\:? \\ $$

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

((12)/L)+((12)/S)=1 (4/L)+(9/S)=(1/2) ⇒(1/L)=(1/(20)) ⇒L=20 h ⇒(1/S)=(1/(30)) ⇒S=30 h large pipe needs 20h, small pipe 30h.

$$\frac{\mathrm{12}}{{L}}+\frac{\mathrm{12}}{{S}}=\mathrm{1} \\ $$$$\frac{\mathrm{4}}{{L}}+\frac{\mathrm{9}}{{S}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\frac{\mathrm{1}}{{L}}=\frac{\mathrm{1}}{\mathrm{20}}\:\Rightarrow{L}=\mathrm{20}\:{h} \\ $$$$\Rightarrow\frac{\mathrm{1}}{{S}}=\frac{\mathrm{1}}{\mathrm{30}}\:\Rightarrow{S}=\mathrm{30}\:{h} \\ $$$${large}\:{pipe}\:{needs}\:\mathrm{20}{h},\:{small}\:{pipe}\:\mathrm{30}{h}. \\ $$

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

yess

$$\mathrm{yess} \\ $$

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