SOLUTION: Tara plans to take a bath but forgets to close the drain. The bath usually takes 10 minutes to fill and 12 minutes to empty. How long will it be before the bath is filled if Tara c

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Tara plans to take a bath but forgets to close the drain. The bath usually takes 10 minutes to fill and 12 minutes to empty. How long will it be before the bath is filled if Tara c      Log On


   

Question 1150208: Tara plans to take a bath but forgets to close the drain. The bath usually takes 10 minutes to fill and 12 minutes to empty. How long will it be before the bath is filled if Tara continues not to notice that the drain is open?
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Tara plans to take a bath but forgets to close the drain.
The bath usually takes 10 minutes to fill 
So the rate is 1 tub per 10 minutes or 1/10 tub per minute

and 12 minutes to empty.
 

So the rate is -1 tub per 12 minutes or -1/12 tub per minute.

How long will it be before the bath is filled
 
Since it fills faster than it empties, it will eventually be filled

Let the time for filling be t.

We use rate∙time = part of tub filled or emptied by both the faucet
and the drain.  Then set that equal to 1 tubfull.

expr%281%2F10%29%2At-expr%281%2F12%29%2At=1

Multiply both sides by LCD = 60

6t-5t=60
t=60

Answer: 60 minutes or 1 hour.

Edwin

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Here is an alternative to the traditional algebraic method for solving problems like this, using the fraction of the job that each "worker" does in 1 minute -- as shown in the response you got from the other tutor.

In my experience a lot of students like this method because it avoids working with fractions.

Look at the amounts of time each worker takes to do the job. The tap fills the tub in 10 minutes; the drain empties it in 12 minutes.

Now consider the least common multiple of those two times, and imagine that we have several tubs to fill.

The LCM of 10 and 12 is 60. Consider what the two workers could do in 60 minutes.

The tap could fill 60/10 = 6 tubs in 60 minutes; the drain could empty 60/12 = 5 tubs in 6 minutes.
So in 60 minutes the number of tubs that could be filled is 6-5 = 1.

And that of course means the one tub can be filled in 60 minutes.

ANSWER: It will take 60 minutes to fill the tub if the drain is left open.