F.4MATHS QUESTION

2008-09-21 8:12 pm

Quadratic Equations in One Unknown

1.It takes 4 hours for two pipes to simultaneously fill up a swimming pool. If one pipe at a time is used to fill up the swimming pool, the smaller pipe would take 6 hours longer than the large pipe. Find the time it would take the large pipe to fill up the swimming pool.

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回答 (1)

用戶10012

2008-09-21 8:32 pm

✔ 最佳答案

Let the larger pipe can fill the pool in x hours.
Time for the smaller pipe = (x + 6) hours.
In one hour, larger pipe alone can fill 1/x of the pool.
Smaller pipe alone can fill 1/(x+6) of the pool.
Two together in 1 hour can fill 1/x + 1/(x +6) of the pool.
Since it takes 4 hours to fill the pool together. In 1 hour, they 1/4 of the pool.
Therefore,
1/x + 1/(x +6) = 1/4
4(x + 6) + 4x = x(x + 6)
4x + 24 + 4x = x^2 + 6x
x^2 - 2x - 24 = 0
(x +4)(x - 6) = 0
x = -4 (rej.) and 6.
So it takes 6 hours for large pipe to fill the pool alone.

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