SOLUTION: 2. with both hot and cold water running a bath tub can be filled in 8 minuts. the drain will empty the tub in 10 minuts. a child turns both faucets and leaves the drain open. how l

Question 689418: 2. with both hot and cold water running a bath tub can be filled in 8 minuts. the drain will empty the tub in 10 minuts. a child turns both faucets and leaves the drain open. how long will it be before the bath tub starts to over flow?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
2. with both hot and cold water running a bath tub can be filled in 8 minuts. the drain will empty the tub in 10 minuts. a child turns both faucets and leaves the drain open. how long will it be before the bath tub starts to over flow?
one pipe can fill a swimming pool in 10 hours. if a second pipe is used
together with the first pipe, the pool can be filled in 6 hours. how long would
it take the second pipe alone to fill the pool?

Since nowhere in the problem is just one of the faucets on and the other off,
we can just speak of the pair of faucet's filling rate.  There is no need to
separate them.

We are given the pair of faucets' filling rate as 1 tub per 8 minutes, or
 or .

We are given the drain's "filling" rate as -1 tub per 10 minutes, or
 or .

[Note that we must make the drain's filling rate negative!]

We let X = the number of hours it takes for the pair of faucets and
the drain to fill the tub.

So we can say the combined filling rate is 1 tub per X hours, or
 or .

The equation comes from:

      .

              ()

Solve that by getting an LCD of 40X

Edwin

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