Please clarify

[Arunlal]

I found this qn in OG. just couldnt understand the last few things...

The Water from an outlet, flowing at a constant rate, can fill a swimming pool in 9 hours. a second outlet can fill the same pool in 5 hours. how long will it take to fill the same pool if both outlet are used together.

together they can fill at the rate of 1/9+1/5= 14/45. ( i could understand this. but couldnt understand the below statements.

" thus when the outlets are used together they fill the pool in 45/14=3.21 hrs"

How is the above derived. i coulodnt understand this. am i missing out on something basic??

[lunarpower]

I found this qn in OG. just couldnt understand the last few things...

The Water from an outlet, flowing at a constant rate, can fill a swimming pool in 9 hours. a second outlet can fill the same pool in 5 hours. how long will it take to fill the same pool if both outlet are used together.

together they can fill at the rate of 1/9+1/5= 14/45. ( i could understand this. but couldnt understand the below statements.

" thus when the outlets are used together they fill the pool in 45/14=3.21 hrs"

How is the above derived. i coulodnt understand this. am i missing out on something basic??

yes, it's pretty basic. it's also very important, so make sure that you learn the following somehow, whether by putting it on a flash card or by ... something:

the TIME taken to perform one job is the RECIPROCAL OF THE RATE at which that job is performed.

so, since the combined rate is 14/45, the time taken to perform one combined job is the reciprocal of that number, or 45/14.

if you want to, you could also derive this number by using a good old fashioned RTD equation: (14/45 pool/hr)(x hours) = 1 pool; therefore, x = 45/14 hour. since the right-hand side is 1 job (1 pool, in this case), you'll notice that this scenario will give you the reciprocal in all cases.

[rohangupta83]

together they can fill at the rate of 1/9+1/5= 14/45. ( i could understand this. but couldnt understand the below statements.

the above statement means that 14 parts of the pool (out of 45 parts in total) can be filled in 1 hour.

so in 1 hour 14/45 parts can be filled

in 2 hours 2X14/45 parts = 28/45 parts can be filled

in 3 hours 42/45 parts can be filled

in 3.21 hours 45/45 parts can be filled = 1 pool

or in another way:

14/45 parts are filled in 1 hour

1 part is filled in 1 hour X 45/14

" thus when the outlets are used together they fill the pool in 45/14=3.21 hrs"

Hope this clears things up.