Question

A farmer can plow a given field in 12 hours. If his son helps him, they can plow the field together in 8 hours. How many hours would it take his son to plow the field alone? Express your answer as a fraction reduced to lowest terms, if needed.

Answer 1

To solve this problem, we need to find the rate at which the farmer and his son plow the field together, and then use this rate to find the number of hours it will take the son to plow the field alone.

Let's call the rate at which the farmer and his son plow the field together R. We know that they can plow the field together in 8 hours, so:

R / 8 hours = 1 field

R / 12 hours = 1/3 field

To find the rate at which the son plows the field alone, we can divide the above equation by 2:

R / 24 hours = 1/3 field

R / 12 hours = 2/3 field

Therefore, it will take his son R/12 = 2/3 hours to plow the field alone. To reduce the answer to lowest terms, we can divide both the numerator and denominator by 2:

R/6 hours

Therefore, it will take the son R/6 = 1/3 hours to plow the field alone.