A pipe P can fill a tank in 12 min and another pipe R canfill it in 15...
And R are filling the tank while the 3rd pipe M is emptying it.
To find the time it takes to fill the tank with all three pipes working together, we need to find the combined rate at which they fill or empty the tank.
Pipe P fills the tank in 12 min, which means it can fill 1/12th of the tank in 1 min.
Pipe R fills the tank in 15 min, which means it can fill 1/15th of the tank in 1 min.
Pipe M empties the tank in 6 min, which means it can empty 1/6th of the tank in 1 min.
To find the combined rate, we add the rates of the filling pipes and subtract the rate of the emptying pipe:
1/12 + 1/15 - 1/6
To simplify this expression, we need to find a common denominator for 12, 15, and 6, which is 60.
1/12 + 1/15 - 1/6 = (5/60) + (4/60) - (10/60) = -1/60
This means that working together, the three pipes can empty 1/60th of the tank in 1 minute.
To find the time it takes to fill the tank, we can take the reciprocal of the combined rate:
1 / (-1/60) = -60/1
The negative sign indicates that the tank is being emptied rather than filled. Therefore, it would take 60 minutes to empty the tank with all three pipes working together.