Answer: it will take 360 minutes to fill the tank.
Explanation:
1. First, let's find the rates at which each pipe fills or discharges the tank.
- The first pipe can fill the tank in 45 minutes, so its filling rate is 1/45 of the tank per minute.
- The second pipe can discharge the tank in one hour, which is equivalent to 60 minutes. Therefore, its discharging rate is 1/60 of the tank per minute.
2. Next, let's determine how long it takes for the tank to be filled when the pipes work on alternate minutes.
- Since the pipes work on alternate minutes, each pipe has 1 minute to either fill or discharge the tank.
- In the first minute, the first pipe fills 1/45 of the tank.
- In the second minute, the second pipe discharges 1/60 of the tank.
- This process continues, with the first pipe filling in odd-numbered minutes and the second pipe discharging in even-numbered minutes.
3. To find out when the tank will be completely filled, we need to calculate how many cycles of alternating minutes are required.
- In each cycle of 2 minutes, the net change in the tank's level is (1/45 - 1/60) of the tank.
- Simplifying this expression, we get (4/180 - 3/180) of the tank, which is 1/180 of the tank.
- Therefore, it takes 180 cycles of alternating minutes to fill the entire tank.
4. Finally, let's calculate the total time required to fill the tank.
- Since each cycle of alternating minutes takes 2 minutes, the total time required is 180 cycles multiplied by 2 minutes per cycle.
- Thus, the tank will be filled in 360 minutes.
Therefore, if both pipes work on alternate minutes,