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?

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