Answer:

Precisely 3 hours, 19 minutes, 12 seconds.

Step-by-step explanation:

I NEVER liked questions like these. INVERSE PROPORTIONS

work rate, w is INVERSELY proportional to time, t

meaning w = K / t where K is a constant representing the amount of work

Now B is a dude whose work rate is well…B, and the time he TAKES to complete K is 6 hours

therefore, B = K / 6

In the second statement, B and C can do the work in 4 hours. This means that the combined work rate of B and C is

B + C = K / 4

now since we know the work rate of B, we have to find that of C

(K / 6) + C = (K / 4)

C = (K / 4) - (K /6)

C = K / 12

C’s work rate is K/12 meaning it would take C 12 hours to complete the work alone

In the third statement, A, B, and C can complete this work in 2.6 hours. As usual,

A + B + C = K / 2.6

Now the mystery man is A, what is his work rate?

A + (K/6) + (K/12)= (K/2.6)

A = (K/2.6) - (K/6) - (K/12)

A = K/7.43

So it takes A, 7.43 hrs to complete the work alone.

Now the question is to find out how LONG A and B would take to complete the work

In order to find this, we have to combine their work rates

A + B = ?

(K/7.43) + (K/6) = K/3.32

So when A and B work together, it would take 3.32 hours to finish

Precisely 3 hours, 19 minutes, 12 seconds.

Unless a meteor crashes