A piston pump with a 5-inch piston and a 10-inch stroke operates at 60 strokes per minute. How many minutes will it take to pump 6,000 gallons?

To determine how long it will take for the piston pump to move 6,000 gallons, we first need to calculate the pump's flow rate.

The volume displaced by one stroke of the piston can be calculated using the formula for the volume of a cylinder, which is:

[ \text{Volume} = \pi \times r^2 \times h ]

where ( r ) is the radius, and ( h ) is the stroke length. Given that the diameter of the piston is 5 inches, the radius is half of that (2.5 inches). The stroke length is given as 10 inches.

First, we convert the measurements to feet for consistency, as there are 12 inches in a foot:

• Radius in feet: ( 2.5 , \text{inches} = \frac{2.5}{12} , \text{feet} \approx 0.2083 , \text{feet} )

• Stroke length in feet: ( 10 , \text{inches} = \frac{10}{12} , \text{feet} \approx 0.8333 , \text{feet} )

Now, we