To fill a swimming pool 2 …
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To fill a swimming pool 2 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 seperately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool.
Posted by Anubhab Majumder 6 years, 9 months ago
- 1 answers
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Sahdev Sharma 6 years, 9 months ago
Let the time taken by the pipe of larger diameter = x hours
The time taken by the pipe of smaller diameter = x + 10 hours
In 1 hour pipe of larger diameter fills {tex}1\over x{/tex}part of the pool , So in 4 hour the pipe of larger diameter fills = {tex}4\over x{/tex}
In 1 hour pipe of smaller diameter fills {tex}1\over x + 10{/tex} part of the pool , So in 9 hour the pipe of larger diameter fills ={tex} 9\over x + 10{/tex}
ATQ
{tex}{4\over x} + {9\over x + 10} = {1\over 2}{/tex}
=> {tex}{4x+40+9x\over x^2+10x}= {1\over 2}{/tex}
=> {tex}x^2+10x = 26x+80{/tex}
=> {tex}x^2-16x-80=0{/tex}
=> {tex}x^2-20x+4x-80=0{/tex}
=> x(x-20)+4(x-20)= 0
=> (x-20)(x+4)=0
x = - 4 and 20,
But we assume x as hour , So we neglect negative term and get
x = 20
The time taken by the pipe of larger diameter = 20 hours
And
The time taken by the pipe of smaller diameter = 20 + 10 = 30 hours
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