Hello!
First, we have to calculate the least common multiple of 12 and 15.
LMC(12, 15) = 60
So, we discovered that the capacity of the cistern equals 60 liters.
Now, let's calculate how many liters of water each tube can fill:
P: 60/12 = 5 liters per minute
Q: 60/15 = 4 liters per minute
Analyzing the exercise:
"They were opened together and the first tube was closed 3 minutes after filling"
As we know when the first tube (P) was closed, let's calculate how much water it filled:
5 liters per minute * 3 minutes = 15 liters of water
Also, let's calculate the same with the second tube (Q) because they're filling together:
4 liters per minute * 3 minutes = 12 liters of water
So, we know that after 3 minutes of filling, the cistern has 15 + 12 = 27 liters of water, right?
Let's calculate how many liters the cistern needs to be full:
60 - 27 = 33 liters
Remember: Now, just tube Q is filling.
33 liters divided by 4 liters per minute:
33/4 = 8.25 minutes remaining to the cistern be full