Three taps A, B ,& C can fill a tank in 12, 15, & 20 hours respectively. If A is open all the tank and B & C are open for one hour each alternatively,the tank will be full in:
Please proofread your question. It doesn't make any sense.
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To solve this problem, we need to determine the combined rate at which taps A, B, and C fill the tank. Once we know the combined rate, we can find out how long it takes for the tank to be filled.
Let's start by finding the individual rates at which taps A, B, and C fill the tank:
- Tap A fills the tank in 12 hours, so its rate is 1/12 tank per hour.
- Tap B fills the tank in 15 hours, so its rate is 1/15 tank per hour.
- Tap C fills the tank in 20 hours, so its rate is 1/20 tank per hour.
Now, let's calculate the combined rate when A, B, and C are open together:
Combined rate = Rate of A + Rate of B + Rate of C
= 1/12 + 1/15 + 1/20
To add these fractions, we need a common denominator, which is 60:
Combined rate = (5/60) + (4/60) + (3/60)
= 12/60
= 1/5 tank per hour
Now that we know the combined rate, let's determine how long it takes for the tank to be filled when A is open all the time, and B and C are open for one hour each alternatively.
In one cycle of A, B, and C being open alternatively, the total time taken is 2 hours (1 hour for B + 1 hour for C).
Since the combined rate is 1/5 tank per hour, the amount of the tank filled in 2 hours is:
Amount of tank filled = Combined rate * Time
= (1/5) * 2
= 2/5 tank
So, in one cycle, the tank is filled 2/5th of its capacity. To fill the entire tank, we need to repeat this cycle multiple times.
Since one cycle takes 2 hours, and each cycle fills 2/5 of the tank, the total number of cycles required to fill the tank can be found by dividing the capacity of the tank by 2/5:
Number of cycles = Tank capacity / (2/5)
= (5/2) * Tank capacity
Given that the tank capacity is 1 (as we are considering the tank to be of unit capacity), the number of cycles required would be:
Number of cycles = (5/2) * 1
= 5/2
= 2.5 cycles
Since we cannot have a fraction of a cycle, we need to round up the number of cycles to the nearest whole number. Therefore, we need a minimum of 3 cycles to fill the tank completely.
Since each cycle takes 2 hours, the total time taken to fill the tank would be:
Total time = Number of cycles * Time per cycle
= 3 * 2
= 6 hours
Thus, if tap A is open all the time, and taps B and C are open for one hour each alternatively, the tank will be full in 6 hours.