SOLUTION: Determine number of acres in a field if the length is to the width as 7 is to 3. A person is walking at 4 mph for an hr. and 15 min. around the field. Not sure how to solve.

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Question 1184129: Determine number of acres in a field if the length is to the width as 7 is to 3. A person is walking at 4 mph for an hr. and 15 min. around the field.
Not sure how to solve.
Found 3 solutions by josgarithmetic, MathTherapy, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Determine number of acres in a field if the length is to the width as 7 is to 3. A person is walking at 4 mph for an hr. and 15 min. around the field.
Not sure how to solve.
Let multiplicative factor for length and width be x

Then length = 7x, and width = 3x

Perimeter of field: 2(7x + 3x) = 2(10x) = 20x

Walking at 4 mph for 1 hour and 15 min, or for matrix%281%2C5%2C+1%261%2F4%2C+hours%2C+%22=%22%2C+5%2F4%2C+hours%29, we get: 

With x being 1%2F4, length = matrix%281%2C3%2C+7%281%2F4%29%2C+%22=%22%2C+7%2F4%29, and width = matrix%281%2C3%2C+3%281%2F4%29%2C+%22=%22%2C+3%2F4%29

Since acreage denotes AREA, we get area as:

Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


Given length:width = 7:3, let the length be 7x and the width 3x.

Then the perimeter is twice (length+width) = 20x.

The person walked around the perimeter in 1 hour and 15 minutes, or 5/4 hours, at 4mph; so the perimeter of the field is (5/4)*4 = 5 miles. Then

20x=5
x=5%2F20+=+1%2F4

The length of the field is 7x=7/4 miles; the width is 3x=3/4 miles. The area is (7/4)(3/4) = 21/16 square miles.

There are 640 acres per square mile, so the number of acres is 640(21/16) = 21*40=840.

ANSWER: 840 acres