lstsch wrote:
chetan2u VeritasKarishmaHello - Why we are able to divide the time by rate to figure out how long it will take to fill 1 pool? "(5/4)/(5/12)∗1=3 hrs"
I thought the formula to calculate the time is: Time = Work/Rate but that gives me 1/3. Thank you very much in advance!
"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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Karishma
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