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?

How long would it take Charles alone to string the same line is 1.5 days

Let x represent How long would it take Charles alone to string the same line

Let  Charles represent  1/x of the line daily

Let John represent 1/3 of the line daily

Let both  John and Charles represent 1/x + 1/3 of the line daily

Now let determine How long would it take

Charles alone to string the same line

Hence:

1/x + 1/3 =1

Multiply both term by 3x

3+x=3x

Divide both side

2x=3

x=3/2

x=1.5 days

Inconclusion How long would it take Charles alone to string the same line is 1.5 days.

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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