Question

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?

Answer 1

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

Answer 2

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

This is because 12x15=180

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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

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Now 15+12=27

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

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Therefore your answer is:

6 hours and 40 mins