Answer:
15 hours.
Explanation:
Let's use the concept of work rates to solve this problem.
Let R be the work rate of the farmer (how much of the field he can plow per hour) and S be the work rate of his son (how much of the field he can plow per hour).
From the information given, we can create the following equations:
The farmer can plow the field in 10 hours, so his work rate is 1/10 of the field per hour.
R = 1/10
When they work together, they can plow the field in 6 hours, so their combined work rate is 1/6 of the field per hour.
R + S = 1/6
Now, we need to find how long it would take the son to plow the field alone, which means finding S.
We already know R from the first equation, so we can substitute it into the second equation:
(1/10) + S = 1/6
Now, let's solve for S:
S = 1/6 - 1/10
To subtract these fractions, we need a common denominator, which is 30:
S = (5/30) - (3/30)
S = (5 - 3)/30
S = 2/30
Simplify the fraction:
S = 1/15
So, the son can plow 1/15 of the field per hour. Now, to find out how many hours it would take him to plow the entire field alone, take the reciprocal of his work rate:
Time = 1 / (1/15)
Time = 15 hours
It would take the son 15 hours to plow the field alone.