Combined rates – Three workers together: A can complete the work in 8 days, B in 10 days, and C in 20 days. If all three work together from the start, in how many days will the work be completed?
Correct Answer: 40/11 days
Introduction / Context:When multiple workers collaborate, their work rates add up. Convert each time to a per-day rate and sum to get the combined rate.
Given Data / Assumptions:
- A alone: 8 days ⇒ 1/8 per day.
- B alone: 10 days ⇒ 1/10 per day.
- C alone: 20 days ⇒ 1/20 per day.
Concept / Approach:Total rate = 1/8 + 1/10 + 1/20. Time = 1 / (total rate).
Step-by-Step Solution:1/8 + 1/10 + 1/20 = 5/40 + 4/40 + 2/40 = 11/40.Time together = 1 / (11/40) = 40/11 days.
Verification / Alternative check:Approximate: 40/11 ≈ 3.636 days, which is reasonable since A alone needs 8 days and others help.
Why Other Options Are Wrong:Fractions like 39/11, 41/11, 32/11, 35/11 do not match the exact rate sum 11/40.
Common Pitfalls:Adding times (8 + 10 + 20) instead of rates; arithmetic errors in common denominators.
Final Answer:40/11 days