Let's denote the amount of work A, B, and C can do in one day as a, b, and c respectively.

From the problem, we know that:

1/a = 3(b + c) (1) (since A takes three times as long as B and C together)

1/b = 4(a + c) (2) (since B takes four times as long as A and C together)

a + b + c = 1/24 (3) (since all three together can complete the job in 24 days)

We can solve these three equations to find the values of a, b, and c.

First, let's multiply equations (1) and (2) to get:

1/(a*b) = 12(a + b + c)

Substitute equation (3) into this to get:

1/(a*b) = 12/24 = 1/2

So, a*b = 2 (4)

Now, let's add equations (1) and (2) to get:

1/a + 1/b = 3(a + b + c) + 4(a + b + c) = 7(a + b + c)

Substitute equation (3) into this to get:

1/a + 1/b = 7/24

So, 1/a = 7/24 - 1/b

Substitute equation (4) into this to get:

1/a = 7/24 - a/2

Solving this equation for a gives:

a = 1/30

So, A alone will take 30 days to finish the job.

Question

Let's denote the amount of work A, B, and C can do in one day as a, b, and c respectively.

From the problem, we know that:

1/a = 3(b + c)   (1)  (since A takes three times as long as B and C together)

1/b = 4(a + c)   (2)  (since B takes four times as long as A and C together)

a + b + c = 1/24  (3)  (since all three together can complete the job in 24 days)

We can solve these three equations to find the values of a, b, and c.

First, let's multiply equations (1) and (2) to get:

1/(a*b) = 12(a + b + c)

Substitute equation (3) into this to get:

1/(a*b) = 12/24 = 1/2

So, a*b = 2   (4)

Now, let's add equations (1) and (2) to get:

1/a + 1/b = 3(a + b + c) + 4(a + b + c) = 7(a + b + c)

Substitute equation (3) into this to get:

1/a + 1/b = 7/24

So, 1/a = 7/24 - 1/b

Substitute equation (4) into this to get:

1/a = 7/24 - a/2

Solving this equation for a gives:

a = 1/30

So, A alone will take 30 days to finish the job.

Knowee AI · Accepted Answer

Let's denote the amount of work A, B, and C can do in one day as a, b, and c respectively.

From the problem, we know that:

1/a = 3(b + c)   (1)  (since A takes three times as long as B and C together)

1/b = 4(a + c)   (2)  (since B takes four times as long as A and C together)

a + b + c = 1/24  (3)  (since all three together can complete the job in 24 days)

We can solve these three equations to find the values of a, b, and c.

First, let's multiply equations (1) and (2) to get:

1/(a*b) = 12(a + b + c)

Substitute equation (3) into this to get:

1/(a*b) = 12/24 = 1/2

So, a*b = 2   (4)

Now, let's add equations (1) and (2) to get:

1/a + 1/b = 3(a + b + c) + 4(a + b + c) = 7(a + b + c)

Substitute equation (3) into this to get:

1/a + 1/b = 7/24

So, 1/a = 7/24 - 1/b

Substitute equation (4) into this to get:

1/a = 7/24 - a/2

Solving this equation for a gives:

a = 1/30

So, A alone will take 30 days to finish the job.

A takes three times as long as B and C together to do a job. B takes four times as long as A and C together to do the work. If all the three, working together can complete the job in 24 days, then the number of days. A alone will take to finish the job is