Question

A takes 4 hours, B 5 hours and C 6 hours to complete a task. How long will it take A and B to do as much work as C does in 4.25 hours?​

Answer 1

Step-by-step explanation:

Let A and B together complete the work in "t" hours

Now, according to question

Work done by A

t + [(1/A) + (1/B)] + 4.5 = (t + 4.5)/A

t/A = 4.5/B

A/B = t/4.5 ----(1)

Similarly work done by B,

t + [(1/A) + (1/B)] + 8 = (t + 8)/B

t/B = 8/A

A/B = 8/t ----(2)

Comparing (1) and (2), we get

t/4.5 = 8/t

t2 = 36

∴ t = 6 hours

∴ A and B will together complete the task in 6 hours