# Three water pipe are used to fill a sw[mming pool.the first pipe alone takes 8 hours to fill the pool,the second pipe alone takes 12 hours to fill the pool and the third pipe alone takes 24 hours to fill the pooll. if all three pipes are opened at the same time, how long will it take all three together to fill the pool?

1
by arjayescobinas

2015-09-18T20:45:16+08:00

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The rate of each pipe to fill the pool alone is the reciprocal of the time.

Rates:
1st pipe - 1/8 per hour
2nd pipe - 1/12 per hour
3rd pipe - 1/24 per hour

Total rate:
1/8 + 1/12 + 1/24
= 3/24 + 2/24 + 1/24
= 6/24
= 1/4 per hour

Distance (the water in the pool) = 1
Rate = 1/4 per hour

Time = Distance/Rate
= 1/(1/4)
= 4 hours

It would take 4 hours if all the pipes were opened at the same time to fill the pool.