Question

To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours
and the pipe of smaller diameter for 9 hours, only half of 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?
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Answer 1

Answer:

Suppose that x hours is the total time taken by the larger pipe and y hours is the total time taken by the smaller pipe .

Now,  

$\frac{4}{x} +\frac{9}{y} =\frac{1}{2}$  --------------------(i)

smaller diameter takes 10 hour more than the larger dia. pipe.

y = x + 10.............(ii)

Put the value eq (i) from eq (ii)

We get, $\frac{4}{x} +\frac{9}{x+10} =\frac{1}{2}$

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

⇒ $26x+80=x^{2} +10x$

=> $x^{2} -16x-80=0$ ------------------(iii)

Solve eq (iii),

(x−20)(x+4)=0

x=20,x=−4

The value of x can not be -ve so that the value of x=20.

So that the larger diameter pipe fill the tank x=20 hour and smaller diameter pipe fill the tank y=x+10=20+10=30 hour

x=20 hour s, y=30 hour s

Hence, the larger pipe takes 20 hours to fill the pool whereas, the smaller pipe takes 30 hours to fill the pool.

Hope it helps.