How Long To Fill The Pool?

The first source fills $\frac{1}{30}$ of the pool per minute, and the second source fills $\frac{1}{90}$ of the pool per minute. Together, they can fill $\frac{1}{30} + \frac{1}{90} = \frac{4}{90}$ of the pool in each minute. Thus, the total number of minutes needed to fill the pool is $\frac{1}{\frac{4}{90}} = \frac{90}{4} = 22.5.$

In 90 minutes, the pool could be filled 4 times over (3 times by the first source and once by the second one). So it must take 90/4 (or 22.5) minutes to fill the pool once

1 / (1 pool / 30min + 1 pool / 90min)

= 22,5 or 22 minutes 30 seconds

Electricity is my specialty so I’ve seen this problem the same way as parallel resistances.

t = (30×90)/120

We'll see that the capacity of the pool is irrelevant, but let's suppose it's needed. We'll set it equal to y. (if numbers work better, 10 is an easy choice).

Pipe A would fill it up in 30 minutes, so it's at a rate of y gallons in 30 mins (y/30). Pipe B would fill it up in 90 minutes, so it's at a rate of y gallons in 90 mins (y/90)

We want to know when our pool will be filled if we use both pipe A and pipe B, which will take x minutes. So we set our equation as (y/30)x + (y/90)x = y

Both terms on the left of the equal sign have a y, therefore we can factor it out.

y[(1/30)x + (1/90)x] = y

We can cancel out the y on the left and right (and have proven that the capacity is irrelevant to how long it'd take to fill).

x/30 + x/90 = 1

We find a common denominator to add the two fractions, which we determine to be 90. Therefore the left term needs to be multiplied by 3/3 to become a fraction with 90 as its denominator.

3x/90 + x/90 = 1

Combining like terms we have

4x/90 = 1

Multiplying both sides by 90/4 (the reciprocal).

(90/4) * (4x/90) = (90/4) * 1

x = 90/4

x= 22.5 minutes.

R1 = 3R2, then filling water with rate = 3R2 + R2 = 4R2 so Time usage = 90/4 = 22.5

Let's take the capacity of the pool as 1000 L.... The rate of filling the water per minute... 1st source: 1000/30=33.3333 ... 2nd source:1000/90=11.1111 .... add both of them... total rate=44.4444... time taken to fill the pool up using both sources= 1000/44.4444=22.5

Just multiple on top and add on the bottom 30*90/(30+90) = 22.5