Venski and his brother have each agreed to mow half of the front lawn, which is a rectangle, 120 feet by 60 feet. The law mower cuts a 4-foot-wide strip. If Venski starts at one corner and mows around the lawn toward the center, on which trip around will he have half the area of the lawn mowed?
area of whole thing is 120x60 = 7200 ft^2
so half of that is 3600 ft^2
make a sketch showing the first run
area of 1st run = 120x4 + 120x4 + 52x4 + 52x4
= 1376
leaving 2224
make a sketch of the remaining rectangle which is 112 by 52
area of 2nd run = 112x4+112x4+48x4+48x4
= 1280
leaving 944
which he will be a able to finish on this 3rd round.
To determine on which trip around the lawn Venski will have half the area mowed, we need to calculate the total area of the lawn and keep track of the area as he mows the lawn strip by strip.
The total area of the lawn is given as 120 feet by 60 feet, which means the total area is 120 * 60 = 7200 square feet.
Since Venski and his brother have agreed to mow half of the front lawn each, each of them will mow an area of 7200 / 2 = 3600 square feet.
Next, we need to determine the area mowed with each strip. The lawn mower cuts a 4-foot-wide strip, so the area mowed with each strip is 4 feet multiplied by the length of the strip, which is equal to the perimeter of the lawn, given that the width of the strip is 4 feet.
To calculate the perimeter, we need to find the length of all four sides of the rectangle. The length of the front and back sides is 120 feet each, while the length of the two sides is 60 feet each.
Multiplying the length of each side by 2 (since there are two sides with the same length), we find:
Front Side: 120 feet * 2 = 240 feet
Back Side: 120 feet * 2 = 240 feet
Left Side: 60 feet * 2 = 120 feet
Right Side: 60 feet * 2 = 120 feet
Now, we can calculate the perimeter by adding up the lengths of all four sides:
Perimeter = Front Side + Back Side + Left Side + Right Side
= 240 feet + 240 feet + 120 feet + 120 feet
= 720 feet.
So, the area mowed with each strip is 4 feet * 720 feet = 2880 square feet.
To determine on which trip around the lawn Venski will have half the area mowed, we divide the total area mowed (3600 square feet) by the area mowed with each strip (2880 square feet):
Number of trips = Total area mowed / Area mowed with each strip
= 3600 square feet / 2880 square feet
≈ 1.25.
Hence, Venski will have half the area mowed on his second trip around the lawn.