Question

To fill a swimming pool two pipes are to be used. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool.

Answer 1

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• Let the total time taken by the larger pipe to fill the tank ⇒  'x hours

• So, in 1 hour it would fill ⇒ $\frac{1}{x}$

• Let the total time taken by smaller pipe  to fill the tank ⇒ 'y' hours
• So, in 1 hour it would fill  ⇒$\frac{1}{y}$

y ⇒ 10 + x -----------------(1)

$\frac{4}{x} +\frac{9}{y} ⇒ \frac{1}{2}$

Substitute Eq.(1) in Eq.(2)

$\frac{4}{x} + \frac{9}{10+x} ⇒ \frac{1}{2}$

x² - 16x -80 ⇒ 0

(x - 20) ( x + 4 ) ⇒ 0

Neglecting x = -4 as time cannot be negative.

∴ Time taken by larger tap ⇒ 20 hours

∴ Time taken by smaller tap ⇒ 30 hours

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