A completes a work in 2 days, B in 4 days, C in 9 days, and D in 18 days. They…
2025
A completes a work in 2 days, B in 4 days, C in 9 days, and D in 18 days. They are split into two groups of two workers each, such that the difference between the two groups' time to complete the work is the maximum possible. What is that maximum difference, in days?
- A.
11/2
- B.
15/7
- C.
10/3
- D.
14/3
Show answer & explanation
Correct answer: D
Concept: When two people work together, their combined rate of work is the sum of their individual rates, so the time for a pair to finish the job together is (t1 x t2) / (t1 + t2). To make the completion times of two 2-person groups as far apart as possible, the two slowest workers should be grouped together (giving the longest time) and the two fastest workers should be grouped together (giving the shortest time).
Individual times: A = 2 days, B = 4 days, C = 9 days, D = 18 days.
Group the two slowest workers, C and D: combined time = (9 x 18) / (9 + 18) = 162/27 = 6 days.
Group the two fastest workers, A and B: combined time = (2 x 4) / (2 + 4) = 8/6 = 4/3 days.
Difference between the two groups' times = 6 - 4/3 = 18/3 - 4/3 = 14/3 days.
Cross-check: adding rates instead of times gives the same result. C and D's combined rate = 1/9 + 1/18 = 1/6 per day, so their time = 6 days; A and B's combined rate = 1/2 + 1/4 = 3/4 per day, so their time = 4/3 days. This matches the values above and confirms this pairing produces the maximum possible difference of 14/3 days.