Question

Tap X can fill a bath in 12 minutes.

Answer 1

Answer:  4 minutes

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Explanation:

Let's say that this tub is 72 gallons. I picked this number since 12*6 = 72. You can pick any number you want, but I picked this number so we end up with whole number results as shown below.

Tap X can fill the 72 gallon tub in 12 minutes. Its rate is 72/12 = 6 gallons per minute. Tap Y has a rate of 12 gallons per minute because 72/6 = 12.

Add the two unit rates: 6+12 = 18

If the two taps are opened at the same time, then they will work at a rate of 18 gallons per minute.

Let x be the number of minutes. The expression 18x represents how much of the tub is full after x minutes. Set this equal to the 72 we started with earlier and solve for x.

18x = 72

x = 72/18

x = 4

It will take 4 minutes if both taps are running at the same time.