中二級數學問題急！！！

2009-03-07 8:18 pm

Set up a simultaneous linear equations to solve the problem.
1)Pipe A takes twice the time to fill up a pool as pipe B does. The
pool can be filled up in 2 hours when both pipes are opened . How
long would it take each pipe to fill the pool up alone?
Let x hours be the time pipe A takes and y hours be the time pipe B
takes to fill the pool up alone.

回答 (1)

老爺子

2009-03-07 8:55 pm

✔ 最佳答案

1)
Let x hours be the time pipe A takes and y hours be the time pipe B takes to fill the pool up alone.

Fraction of the pool that filled up by pipe A in 1 hour = 1/x
Fraction of the pool that filled up by pipe B in 1 hour = 1/y

Pipe A takes twice the time to fill up a pool as pipe B does:
x = 2y ...... (1)

1/2 of the pool is filled up when both pipes are opened:
1/x + 1/y = 1/2 ...... (2)

Put (1) into (2)
1/2y + 1/y = 1/2
1/2y + 2/2y = 1/2
3/2y = 1/2
2y = 6
y = 3

Put y = 3 into (1):
x = 2 x (3)
x = 6

Pipe A takes 6 hours to fill up the pool, and pipe B takes 3 hours.
=

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