Tap 1 fills the pool in 12 hours, while tap 2 fills the same pool in 15 hours. how long does it take to fill this pool if both taps are used?

Ok, so what we can do is divide the volume of the pool up into 180 parts.

This is because 12x15=180



So every hour, Tap 1 fills up 15/180 of the pool.

*Note that 12 x 15/180 = 180/180

And every hour, Tap 2 fills up 12/180 of the pool.

*Note that 15 x 12/180 = 180/180



Now 15+12=27

27 fits into 180, 6 and 2/3 times.



Therefore your answer is:

6 hours and 40 mins

Tap-1 fills 1/12 of the pool each hour.
Tap-2 fills 1/15 of the pool each hour.
Pouring together, they fill  (1/12 + 1/15) of the pool each hour.
How much is that ?  Can you add those fractions ?

In order to add fractions, they need a common denominator.
The smallest common denominator for 12ths and 15ths is 60ths.

           (1/12 + 1/15)  =  (5/60 + 4/60)  =  9/60 pool per hour, together.

The unit rate of  9/60 pool per hour is the same thing as  60/9 hour  per pool. 

       60/9 hour =  (6 and 2/3) hours per pool  or  6hrs 40minutes

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