Jane ran around the perimeter of a rectangular park at a constant rate of 10 feet per second. The park has an area of 67,500 square feet, and its length is exactly three times its width. For how many seconds did Jane run?
F. 60
G. 120
H. 240
J. 360
K. 480
the park is 150 by 450, making a perimeter of 1200 ft
1200/10 = 120 seconds
G
Can you show me how to solve it, please.
Thank you very much, Steve.
To solve this problem, we need to find the length and width of the park and then calculate the perimeter.
Let's denote the width of the park as "w". According to the problem, the length is three times the width, so the length would be 3w.
To find the values of w and 3w, we can use the area of the park, which is given as 67,500 square feet. The formula for calculating the area of a rectangle is A = l × w, where A represents the area, l represents the length, and w represents the width.
Substituting the values we have, 67,500 = 3w × w.
Simplifying this equation, we get: 67,500 = 3w^2.
Dividing both sides of the equation by 3, we get: 22,500 = w^2.
Taking the square root of both sides, we get: w = √22,500.
Calculating the square root, we find that w ≈ 150.
Since the length is three times the width, the length would be 3 × 150 = 450.
To find the perimeter of the park, we use the formula P = 2l + 2w, where P represents the perimeter.
Substituting the values we have: P = 2 × 450 + 2 × 150 = 900 + 300 = 1200.
Now, we need to find the time Jane took to run around the perimeter. Since her rate is given as 10 feet per second, the time it took her to run around the park is:
Time = Distance / Rate = Perimeter / Rate = 1200 / 10 = 120 seconds.
Therefore, Jane ran for 120 seconds.
The correct answer is G. 120.