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Question

It can take $$12$$ hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for four hours and the pipe of smaller diameter for $$9$$ hours, only half of the pool can be filled. How long would it take for each pipe to fill the pool separately?


Solution

Let the total volume of the pool be 'V',
let 'U' and 'u' be the velocity of water coming out from the pipes with bigger and smaller diametre respectively,
and,
 'A' and 'a' be their respective cross sectional area,
therefore,
$$12[au +AU]=V$$ ...........  given_________(1).
and,
$$4AU+9au=\dfrac{V}{2}$$  .........  given________(2).
From equation (1) and (2), and by taking unit time,
$$AU=\dfrac{V}{20}$$   ______(3).
and,   $$au=\dfrac{V}{30}$$   _______(4).

Time taken by pipe with bigger diametre to fill the pool is:-
$$T.AU= V$$  ............from eq. (3).
=> $$T=20 hour$$
Time taken by pipe with smaller diametre to fill the pool is:-
$$T.au=V$$  ...........from eq. (4).
=> $$T=30hour$$


Mathematics

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