Amar, Akbar, and Anthony are working on a project. Working together Amar and Akbar can complete the project in 1 year, Akbar and Anthony can complete in 16 months, Anthony and Amar can complete in 2 years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is

To solve this problem, we need to first understand that the rate of work done is reciprocal to the time taken to complete the work.

1. Amar and Akbar can complete the work in 1 year, so their combined rate of work is 1/1 = 1 work/year.
2. Akbar and Anthony can complete the work in 16 months or 4/3 years, so their combined rate of work is 1/(4/3) = 3/4 work/year.
3. Anthony and Amar can complete the work in 2 years, so their combined rate of work is 1/2 work/year.

Let's denote the individual rates of work for Amar, Akbar, and Anthony as A, B, and C respectively. We can then write the following equations based on the information given:

1. A + B = 1
2. B + C = 3/4
3. C + A = 1/2

Adding all these equations together gives 2A + 2B + 2C = 1 + 3/4 + 1/2 = 9/4. Dividing both sides by 2 gives A + B + C = 9/8. This is the total rate of work if all three work together.

Subtracting the second equation (B + C = 3/4) from this result gives A = 9/8 - 3/4 = 3/8. This is Amar's rate of work.

Subtracting the third equation (C + A = 1/2) from the total rate of work gives B = 9/8 - 1/2 = 5/8. This is Akbar's rate of work.

Finally, subtracting the first equation (A + B = 1) from the total rate of work gives C = 9/8 - 1 = 1/8. This is Anthony's rate of work.

So, Amar is the fastest worker, Anthony is the slowest, and Akbar is neither the fastest nor the slowest. If Akbar works alone, the time he will take to complete the project is the reciprocal of his rate of work, which is 1/(5/8) = 8/5 = 1.6 years or 1 year and 7.2 months (approximately 1 year and 7 months).