Question

A farmer can plow a given field in 11 hours. If his son helps him, they can plow the field together in 6 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

Answer:

13 1/5hours

Step-by-step explanation:

If the man can plough a given field in 11hours, this means the man can plough 1/11 of the same field in 1hour.

Let 1/x be the portion of the land the son can plough in 1 hour where x is the number of hours the son can plough the land alone.

If they can plough the field together in 6 hours, it means they can plough 1/6 portion of the field together in 1 hour.

Mathematically,

t/11+t/x = 1

Where t is the total time it takes them to plough the land together

Finding the LCM we have;

xt+11t/11x = 1

xt + 11t = 11x

If t = 6

6x +11(6) = 11x

66 = 11x -6x

66 = 5x

x = 66/5

x = 13 1/5hours

This means it will take the son 13 1/5hours to plough the land alone.