To answer the question of how long it takes to fill a water tank of 4,000 liters capacity, let's break down the process step by step:
1. Convert the Filling Time to Hours:
- The given time to fill 6,000 liters is 3 hours and 74 minutes. Since 74 minutes can be converted to hours by dividing by 60, we can represent the filling time as:
[tex]\[
\text{Total time in hours} = 3 + \frac{74}{60}
\][/tex]
- Converting 74 minutes to hours:
[tex]\[
\frac{74}{60} = 1.2333 \, \text{hours} (approximately)
\][/tex]
- Adding this to the initial 3 hours:
[tex]\[
\text{Total time in hours} = 3 + 1.2333 = 4.2333 \, \text{hours} (approximately)
\][/tex]
2. Calculate the Rate of Flow:
- The rate at which water flows from the tap can be determined by dividing the total amount of water by the total time taken to fill it:
[tex]\[
\text{Rate of flow} = \frac{6000 \, \text{liters}}{4.2333 \, \text{hours}}
\][/tex]
- When calculated, this gives us:
[tex]\[
\text{Rate of flow} \approx 1417.32 \, \text{liters per hour}
\][/tex]
3. Calculate the Time to Fill a 4,000-Liter Tank:
- To find out how long it will take to fill a tank of 4,000 liters, we divide the tank's capacity by the rate of flow:
[tex]\[
\text{Time to fill the tank} = \frac{4000 \, \text{liters}}{1417.32 \, \text{liters per hour}}
\][/tex]
- When calculated, this gives us:
[tex]\[
\text{Time to fill the tank} \approx 2.8222 \, \text{hours}
\][/tex]
Therefore, the tap has a flow rate of approximately 1417.32 liters per hour and it takes approximately 2.8222 hours to fill a 4,000-liter tank completely.
