Question

18. If an apprentice can do a piece of work in 24 days, and the apprentice and

instructor together can do it in 6 days, how long would it take the instructor to do
the work alone?
18. If an apprentice can do a piece of work in 24 days, and the apprentice and
instructor together can do it in 6 days, how long would it take the instructor to do
the work alone?

Answer 1

The instructor would take 8 days to do the work alone.

Step-by-step explanation:

To solve this problem, let's let x represent the number of days it would take the instructor to do the work alone. We can set up two equations based on the given information:

Equation 1: Apprentice's rate = 1 job / 24 days = 1/24 job per day

Equation 2: Apprentice and instructor's combined rate = 1 job / 6 days = 1/6 job per day

We can set up the following equation to represent the combined rate:

1/24 + 1/x = 1/6

To simplify this equation, we multiply both sides by 24x to eliminate the fractions:

x + 24 = 4x

Now, we can solve for x by subtracting x from both sides and then dividing by 3:

24 = 3x

x = 8

Therefore, it would take the instructor 8 days to do the work alone.

Answer 2

the number of days when instructor do the work alone is 8 days

Step-by-step explanation:

Given that

The apprentice can do the work in 24 days

And, the apprentice and instructor together can do it in 6 days

We need to find out the number of days when instructor do the work alone

So,

`= (1)/(6) - (1)/(24) \\\\= (4 - 1)/(24) \\\\= (3)/(24) \\\\= (1)/(8) \\\\= 8`

hence, the number of days when instructor do the work alone is 8 days