To determine how long it will take to fill a 52,000-gallon tank with a pump that delivers water at a rate of 200 gallons per minute, follow these steps:
1. Calculate the time required in minutes:
- The tank's capacity is 52,000 gallons.
- The pump rate is 200 gallons per minute.
To find the number of minutes required to fill the tank, divide the tank capacity by the pump rate:
[tex]\[
\text{Time in minutes} = \frac{\text{Tank Capacity}}{\text{Pump Rate}} = \frac{52,000}{200} = 260 \text{ minutes}
\][/tex]
2. Convert minutes into hours and minutes:
- There are 60 minutes in one hour.
To find the number of hours, perform integer division by 60:
[tex]\[
\text{Time in hours} = \left\lfloor \frac{260}{60} \right\rfloor = \left\lfloor 4.333 \right\rfloor = 4 \text{ hours}
\][/tex]
The remaining minutes can be found using the modulus operator:
[tex]\[
\text{Remaining minutes} = 260 \mod 60 = 20 \text{ minutes}
\][/tex]
Therefore, a 52,000-gallon tank will be filled in 4 hours and 20 minutes.
