A can do a job in 5 hours, B in 9 hours, and C in 15 hours. If C works with A and B for only 1 hour, how much additional time will A and B together take to finish the remaining work?

Introduction / Context:Mixed participation problems require computing the work done during a short collaborative interval, then finishing with the subset at their combined rate.

Given Data / Assumptions:

• A alone: 5 hours ⇒ rate 1/5 per hour.
• B alone: 9 hours ⇒ rate 1/9 per hour.
• C alone: 15 hours ⇒ rate 1/15 per hour.
• All three work together for the first 1 hour, then only A and B continue.

Concept / Approach:Compute work completed in the first hour by A, B, and C. Subtract from 1 to find the remaining work. Divide the remainder by the combined rate of A and B to get the extra time.

Step-by-Step Solution:

Verification / Alternative check:Compute total time: 1 hour with all three plus 2 more hours with A and B equals 3 hours overall; check that total work equals 1 by summing hourly outputs.

Why Other Options Are Wrong:3, 3.5, 4, 2.5 hours result from arithmetic slips in the fractional sums or dividing remaining work by only one worker’s rate.

Common Pitfalls:Forgetting that only A and B continue after 1 hour; mixing up addition of times versus addition of rates; reducing 17/45 incorrectly.

Final Answer:2 hours