If I have two mowers that travel at a rate of 250 ft per minute and one has a 48 inch cut and the other is a [blank] cut. How much faster could I cut a yard that is 200 foot by 300 foot with the larger mower.
To answer this question, we need to calculate the area of the yard and the cutting time for each mower.
First, let's calculate the area of the yard. The yard is rectangular with dimensions 200 ft by 300 ft. The area is calculated by multiplying the length by the width:
Area of the yard = length * width = 200 ft * 300 ft = 60,000 square feet.
Next, let's calculate the cutting time for each mower. We know that the first mower has a cutting width of 48 inches, but we don't have the cutting width for the second mower.
To find the cutting time, we need to divide the total area of the yard by the area that each mower can cut in one minute. The cutting width is given in feet, so we need to convert it to square feet.
The cutting width of the first mower is 48 inches, which is equal to 4 feet (since there are 12 inches in a foot). The area that the first mower can cut in one minute is:
Area cut by the first mower in 1 minute = mowing rate * cutting width
= 250 ft/min * 4 ft = 1,000 square feet.
Since we don't have the cutting width for the second mower, let's call it "X." The area that the second mower can cut in one minute is:
Area cut by the second mower in 1 minute = mowing rate * cutting width
= 250 ft/min * X ft.
Now, let's calculate the time it takes for each mower to cut the entire yard:
Time taken by the first mower = Total area of the yard / Area cut by the first mower in 1 minute
= 60,000 square feet / 1,000 square feet/minute
= 60 minutes.
Time taken by the second mower = Total area of the yard / Area cut by the second mower in 1 minute
= 60,000 square feet / (250 ft/min * X ft).
To determine how much faster the larger mower can cut the yard compared to the first mower, we need to compare their cutting times:
Difference in cutting time = Time taken by the first mower - Time taken by the second mower.
To find the value of X (the cutting width for the second mower), we need more information. Once we have the value of X, we can calculate the difference in cutting time.