Word Problem – Rates Work and Time

If A and B together can complete a work in 4 days, B and C together in 6 days, C and A together in 5 days, then working individually, who will finish the work in the least time and in how many days?

Answer: A, 120/17 days

Explanation:

Let the rates at which A, B and C work be a, b and c respectively.

Therefore,

a + b = ¼

b + c = 1/6

c + a = 1/5

Solving for a, b and c, we get

a = 17/120

b = 13/120

c = 7/120

As we can see, the rate at which A works is the greatest. Hence A would finish the work in the least time and in 120/17 days.