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p and q fill a pool at a constant rate of 60 litres per minute and 40 litres/m respectively.the pool can be filled in 50 minutes, 75 minutes or 30 minutes,depending on whether pipe p alone pipe, pipe q alone or both pipes p and q are used.if the pool is filled using pipe p alone 1/3 of the time and , both pipes for the rest of the time, how many minutes does ir take to fill the pipe?

Note: In the USA, the volume is converted to liters, for that is how it is spelled over here.

It is know that p fills the pool at 60 liters per minute and q fills the pool at 40 liters (L) per minute (M). I use capital letters since using lowercase would make the l resemble a 1 to closely.

First, to check things out and make it clear what we are doing ...

Since it takes 50 minutes for p, 50M * 60 L/M = 3,000 liters.

Since it takes 75 minutes for q, 75Mm * 40 L/M = 3,000 liters.

Since it takes 30 minutes for both, 30M *(60+40)L/M = 3,000 liters.

Let T be the time to fill and t be the amount of time passed.

What we have is 60 * T/3 + 75 * 2T/3 = 3,000.

That multiplies out to 20T + 50T = 3,000.

Since 20T + 50T = 70T, and we have 70T = 3,000, then T = 300/7 or 42 6/7.

Yes, that's the answer: T = 42 6/7 minutes.

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