A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If the field has a length that is twice its width, find the area of the field in square meters. Do not include units in your final answer, or spaces or commas.
Question
A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If the field has a length that is twice its width, find the area of the field in square meters. Do not include units in your final answer, or spaces or commas.
Solution
Sure, let's solve this step by step:
Step 1: Convert the time from minutes to hours. 30 minutes = 0.5 hours
Step 2: Calculate the total distance jogged. The person jogged at a rate of 12 kilometers per hour for 0.5 hours, so the total distance jogged is 12 km/hr * 0.5 hr = 6 kilometers.
Step 3: Convert the total distance from kilometers to meters. 6 kilometers = 6000 meters
Step 4: Calculate the perimeter of the field. The person jogged 10 times around the field, so the perimeter of the field is 6000 meters / 10 = 600 meters.
Step 5: Set up an equation for the perimeter of the field. The field is rectangular and its length is twice its width. If we let the width be x, then the length is 2x. The perimeter of a rectangle is 2(length + width), so we have the equation 2(x + 2x) = 600.
Step 6: Solve the equation for x. Solving the equation gives x = 100.
Step 7: Calculate the area of the field. The area of a rectangle is length * width, so the area of the field is 2x * x = 2(100 m) * 100 m = 20000 square meters.
So, the area of the field is 20000.
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