John and Charles are linemen. John can string 10 miles of line in 3 days while together they can string it in 1 day. How long would it take Charles alone to string the same line?

It will take Charles 1.5 days

Step-by-step explanation:

The equation for work

1/A + 1/B = 1/C

Where A is the time for the first person to do the job alone

B is the time for the second person to do the job alone

C is the time for both people to do the job together

It will take John 3 days

It will take John and Charles 1 day together

1/3 + 1/B = 1/1

1/3 + 1/B = 1

We need to solve for B

Subtract 1/3 from each side

1/3 + 1/B - 1/3 = 1-1/3

1/B = 2/3

Using cross products

2B = 3*1

Divide each side by 2

2B/2 = 3/2

B = 3/2

It will take Charles 1.5 days