A spray rig moving at 3 mph delivers 44 gallons per acre when the nozzles on the rig are 20 inches apart.
a) Suppose the number of nozzles were increased so that they were only 15 inches apart. Find the new delivery rate of the rig.
b) How could this revised delivery rate be achieved by changing the speed of the rig instead of the spacing of the nozzles?
a) To find the new delivery rate of the spray rig when the nozzles are 15 inches apart, we can use the concept of linear relationships.
The original spray rig had a delivery rate of 44 gallons per acre when the nozzles were 20 inches apart.
Let's assume that the delivery rate is directly proportional to the distance between the nozzles. This means that if we decrease the distance between the nozzles, the delivery rate will increase in the same proportion.
To find the new delivery rate, we need to determine the ratio between the new distance (15 inches) and the original distance (20 inches), and then multiply it by the original delivery rate (44 gallons per acre).
The ratio between the new distance and the original distance is:
(15 inches / 20 inches) = 0.75
So, the new delivery rate is:
0.75 * 44 gallons per acre = 33 gallons per acre
Therefore, the new delivery rate of the rig when the nozzles are 15 inches apart is 33 gallons per acre.
b) To achieve the same revised delivery rate by changing the speed of the rig instead of the spacing of the nozzles, we need to consider the relationship between speed and delivery rate.
Assuming that the delivery rate is directly proportional to the speed of the rig, increasing the speed will result in a proportional increase in the delivery rate.
Let's assume that the original speed of the rig is 3 mph and the original delivery rate is 44 gallons per acre.
To find the new delivery rate, we need to determine the ratio between the new speed and the original speed, and then multiply it by the original delivery rate.
Since we want to maintain the revised delivery rate of 33 gallons per acre (as found in part a), we can set up the following equation:
(Revised Delivery Rate) = (New Speed / Original Speed) * (Original Delivery Rate)
33 gallons per acre = (New Speed / 3 mph) * 44 gallons per acre
We can solve this equation for the new speed:
New Speed = (33 gallons per acre * 3 mph) / 44 gallons per acre
New Speed ≈ 2.25 mph
Therefore, to achieve the revised delivery rate of 33 gallons per acre, the speed of the rig needs to be approximately 2.25 mph.