Question

Working together a small pipe and large pipe can fill a big pool in 6 hour. It takes the smaller pipe 5 hours longer than the large pipe to fill the big pool working alone. How long does it take the smaller pipe to fill the pool by itself ?

Answer 1

The time taken for the smaller pipe to fill the pool by itself is 15.71 hours

Rate of work

• Time taken for both pipes = 6 hours
• Time taken for long pipe = x
• Time taken for small pipe = x + 6

• Rate of work of both pipes = 1/6
• Rate of work of long pipe = 1/x
• Rate of work of small pipe = 1/x + 6

1/6 = 1/x + 1/(x+6)

1/6 = (x+6)+(x) / (x)(x+6)

1/6 = (x+6+x) / x²+6x

1/6 = (2x+6)(x² + 6x)

• cross product

1(x² + 6x) = 6(2x+6)

x² + 6x = 12x + 36

x² + 6x - 12x - 36 = 0

x² - 6x - 36 = 0

• Using quadratic formula

x = 9.71 or -3.71

The value of x cannot be negative

Therefore, the

Time taken for long pipe = x

= 9.71 hours

Time taken for small pipe = x + 6

= 9.71 + 6

= 15.71 hours

Learn more about rate of work:

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