An irrigation pump can pump 250 liters of water per minute. How many hours should the system work to water a rectangular field 75 m by 135 m to a depth of 3 cm?

V=75• 135•0.03=303.75 m³= 303750 L

t=V/V₀=303750/250=1215 min=20.25 hours

To find the time required to water the field, we need to calculate the total volume of water needed and then divide it by the irrigation pump's pumping rate.

First, let's calculate the volume of water needed to cover the field. The formula to calculate the volume of a rectangular block is length × width × height (or depth). In this case, the length is 75 m, the width is 135 m, and the height (depth) is 0.03 m (since 3 cm equals 0.03 m).

Volume of water needed = length × width × depth
Volume = 75 m × 135 m × 0.03 m
Volume = 303.75 cubic meters

Now, we need to convert the volume from cubic meters to liters, since the pumping rate is given in liters per minute. To convert cubic meters to liters, we multiply by 1000 (since 1 cubic meter equals 1000 liters).

Volume in liters = Volume in cubic meters × 1000
Volume in liters = 303.75 m³ × 1000
Volume in liters = 303,750 liters

Now, we can calculate the time required to pump 303,750 liters of water using the pumping rate of 250 liters per minute.

Time (in minutes) = Volume in liters / pumping rate
Time = 303,750 liters / 250 liters per minute
Time = 1215 minutes

Finally, to convert the time from minutes to hours, we divide by 60 (since there are 60 minutes in an hour).

Time (in hours) = Time in minutes / 60
Time = 1215 minutes / 60
Time = 20.25 hours

Therefore, the system should work for approximately 20.25 hours to water the rectangular field to a depth of 3 cm.