Question 1150208
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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.<br>
In my experience a lot of students like this method because it avoids working with fractions.<br>
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.<br>
Now consider the least common multiple of those two times, and imagine that we have several tubs to fill.<br>
The LCM of 10 and 12 is 60.  Consider what the two workers could do in 60 minutes.<br>
The tap could fill 60/10 = 6 tubs in 60 minutes; the drain could empty 60/12 = 5 tubs in 6 minutes.<br>  So in 60 minutes the number of tubs that could be filled is 6-5 = 1.<br>
And that of course means the one tub can be filled in 60 minutes.<br>
ANSWER: It will take 60 minutes to fill the tub if the drain is left open.<br>