Question 1204620
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This kind of "working together" problem, with two workers working at different rates, is so common that it might be useful to learn the short answer:<br>
If two workers alone take A hours and B hours to complete a job, then the number of hours it takes them to do the job together is {{{(AB)/(A+B)}}}.<br>
Of course the unit of time is not relevant -- it could be minutes, or years, or milliseconds....<br>
So for this problem the quick answer is 80/18 = 40/9 minutes.<br>
For another easy way to solve this kind of problem, consider the least common multiple of the two given times.  For this problem, with the two times being 10 and 8 minutes, the least common multiple is 40 minutes.<br>
Now consider the amount of work the two taps could do in 40 minutes.  The hot water tap could fill the tub 40/10 = 4 times; the cold water tap could fill the tub 40/8 = 5 times.<br>
So in 40 minutes the two taps together could fill the tub 4+5 = 9 times; so the number of minutes it takes them together to fill the one tub is 40/9.<br>
ANSWER: 40/9 minutes<br>