Let's break down and solve this problem step-by-step.
### Part (a)
Question: In how many days does the tap fill 15,000 liters of water if it is opened for 3 hours a day?
1. Calculate the rate of water filling per hour:
- The tap fills 6000 liters in 3 days, with 2 hours of operation each day.
- Total hours of operation in 3 days = 3 days 2 hours/day = 6 hours.
- Therefore, the rate of water filling per hour = 6000 liters / 6 hours = 1000 liters/hour.
2. Calculate the number of days needed to fill 15,000 liters with 3 hours of operation each day:
- If the tap is opened for 3 hours a day, it fills 1000 liters/hour 3 hours/day = 3000 liters/day.
- Total days required to fill 15,000 liters = 15,000 liters / 3000 liters/day = 5 days.
### Part (b)
Question: How much water does the tap fill in 7 days if it is opened 4 hours a day?
1. Calculate the amount of water filled in 7 days with 4 hours of operation each day:
- With the rate of 1000 liters/hour, if the tap is opened for 4 hours a day, it fills 1000 liters/hour 4 hours/day = 4000 liters/day.
- Therefore, in 7 days, the total amount of water filled = 4000 liters/day 7 days = 28,000 liters.
### Part (c)
Question: For how many hours is the tap opened every day to fill 35,000 liters of water in 7 days?
1. Calculate the number of hours needed each day to fill 35,000 liters in 7 days:
- In 7 days, a total of 35,000 liters needs to be filled.
- The daily amount of water filled should be 35,000 liters / 7 days = 5000 liters/day.
- Since the rate is 1000 liters/hour, the number of hours the tap needs to be opened each day to achieve 5000 liters/day is 5000 liters/day / 1000 liters/hour = 5 hours/day.
### Summary
1. The tap fills 15,000 liters of water in 5 days if opened for 3 hours each day.
2. The tap fills 28,000 liters of water in 7 days if opened for 4 hours each day.
3. The tap needs to be opened for 5 hours every day to fill 35,000 liters in 7 days.
