The time elapsed between 1/3 full pool and 3/4 full pool is 5/4 hrs. This means 3/4 - 1/3 = 5/12 of the pool was filled in 5/4 hrs.

Again, (5/12)th of the pool will be filled in 5/4 hrs

1 pool will be filled in \(\frac{5/4}{5/12} * 1 = 3\) hrs
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I was with you up until 5/12th of the pool. How did you get the in 1 hour it fills 1/3 of the poor?

A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was 1/3 full, and 1 1/4 hours later it was 3/4 full. What was the total number of hours that it took the pump to fill the pool?

(3/4) - (1/3) = 5/12. 5/12 of the pool was full in 1 1/4 hours time (5/4 hours). To determine a rate of filling we divide how much is full by the time. That is (5/12) ÷ (5/4) = 1/3. This means it fills a pool in 3 hours.

A. 2 1/3
B. 2 2/3
C. 3
D. 3 1/2
E. 3 2/3

I got as far as finding 5/12- though where are you getting 3 hours? Is it the reciprocal of 1/3?

Since it took 1¼ = 5/4 hours to fill 3/4 - 1/3 = 9/12 - 4/12 = 5/12 of the pool, we can let x = the number of hours to fill the pool and create a proportion to determine how long it will take to fill the entire pool.

(5/4)/(5/12) = x/1

5/4 = 5x/12

60 = 20x

x = 3

Answer: C
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We have only one variable (volume of the pool) so let us assume the volume of the pool is 12 liters

At noon, the pool is 4 L (1/3 x 12 L) full, we do not know the time it took to fill 4 L of the pool at this point

At 1:15 pm (75 mins later), the pool is 9 L (3/4 x 12 L) full =====> Rate = (9 - 4) L/75 mins = 1/15 L/min

Therefore, it took 60 mins (4 L x 15 L/min) to fill the 4 L at noon

Time it took to fill the remaining 3 L (remember we assumed the pool is 12 L?) is 45 mins (3 L * 15 L/min)

Therefore, the total time it took to fill the pool = 60 + 75 + 45 = 180 minutes = 3 hours (Answer choice C)

"The time elapsed between 1/3 full pool and 3/4 full pool is 5/4 hrs. This means 3/4 - 1/3 = 5/12 of the pool was filled in 5/4 hrs.

Again, (5/12)th of the pool will be filled in 5/4 hrs"

I am guessing you understand this part. Rest is all application the formula Work = Rate*Time only. Here is how:

(5/12)th of the pool (this is amount of work done - amount of pool filled) will be filled in (5/4) hrs (this is time taken for this work done)

So constant RATE of filling pool = Work / Time = (5/12) / (5/4)

Now, this is the constant rate. We want the time taken to fill 1 pool (work to be done is 1)

Time taken to fill 1 pool = Work / Rate = 1 / ((5/12) / (5/4) = (5/4) / (5/12)

Note what is the work done and time taken in each case. You have been given time taken (5/4 hrs) for certain amount of work (5/12th pool) first. You use this to get the rate of filling. Then you use the rate to find the time taken to do a different amount of work (1 pool). So you apply the formula twice.

In my explanation, I have simply used the direct variation between work and time to get the answer. Knowing that rate is constant, I say:

A amount of work is done in time T.
B amount of work will be done in (T/A)*B

e.g. 1/2 work is done in 2 hrs
1 full work will be done in 2/(1/2) * 1 = 4 hrs
If work doubles, time taken doubles too.
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