Tap A can fill a tank in 8 hrs and tap B can fill the same tank in 6 hrs. If tap B and C are opened at the same time they will fill the tank in half time as tap A. How much time will tap C take to fill the tank alone?
Question
Tap A can fill a tank in 8 hrs and tap B can fill the same tank in 6 hrs. If tap B and C are opened at the same time they will fill the tank in half time as tap A. How much time will tap C take to fill the tank alone?
Solution
Step 1: Determine the rate at which each tap fills the tank.
Tap A fills the tank in 8 hours, so its rate is 1/8 of the tank per hour. Tap B fills the tank in 6 hours, so its rate is 1/6 of the tank per hour.
Step 2: Determine the combined rate of taps B and C.
According to the problem, taps B and C together fill the tank in half the time it takes tap A, which is 8/2 = 4 hours. So, their combined rate is 1/4 of the tank per hour.
Step 3: Determine the rate at which tap C fills the tank.
We know that the combined rate of taps B and C is 1/4 of the tank per hour, and we know that tap B's rate is 1/6 of the tank per hour. Therefore, we can find tap C's rate by subtracting tap B's rate from the combined rate:
1/4 - 1/6 = 1/12
So, tap C fills the tank at a rate of 1/12 of the tank per hour.
Step 4: Determine how long it takes tap C to fill the tank.
Since tap C fills the tank at a rate of 1/12 of the tank per hour, it will take 12 hours for tap C to fill the tank alone.
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