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 la
rge pipe to fill the big pool working alone. How long does it take the smaller pipe to fill the pool by itself ?
1 answer:
The time taken for the smaller pipe to fill the pool by itself is 15.71 hours
<h3>Rate of work</h3>
- 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)
1(x² + 6x) = 6(2x+6)
x² + 6x = 12x + 36
x² + 6x - 12x - 36 = 0
x² - 6x - 36 = 0
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
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