Question

Mr. Boll can pick a bale of cotton by hand in 5 days. If his son joins him in the work, they can pick a bale in 3 days. How long would the son take to do the job?

Answer 1

Answer: 7 1/2 days

(I wanted to answer the way I think the lesson provided)

Explanation:

Mr. Boll can pick a bale of cotton by hand in 5 days. If his son joins him in the work, they can pick a bale in 3 days. How long would the son take to do the job?

The breakdown

1/5 = the part done by Mr. Boll by himself

3/5 = the part done by Mr. Boll in 3 days

1/x = the part done by the son in 1 day

3/x = the part done by the son in 3 days

So, we take the part done by Mr. Boll and the part done by the son and add them. They will = the whole or 1 one the other side of the equation.

3/5 + 3/x =1

Move all terms not containing x to the right side of the equation.

3/x = 1 - 3/5

3/x = 2/5

Find the LCD for both fractions which is 5x to get rid of the denominators. Then multiply both sides by 5x to get rid of them.

3/x (5x) = 2/5 (5x)

15 = 2x

Isolate x by dividing 2 by both sides

15/2 = x

Switch the problem so x in front (my preference)

x = 15/2

Simplify

x = 7 ½ days

Answer 2

okay so first you know that the dad can do it in 5 days and together they can do it in 3. so that's 1/5 for the dad and 1/3 together and x for the son. so the equation would be 1/5 + 1/x = 1/3. Then subtract 1/5 to the other side and that would be 2/15, then multiply the x to 2/15 so the equation now would be
1 =(2/15)x. The final answer is 15/2 which is 7 1/2 days.