A is thrice as efficient as B and therefore finishes the job 60 days earlier than B. How long will A and B take to finish the job working together?

Problem restatement
Relate the individual times using the efficiency ratio and the given 60-day difference, then compute the combined time.

Given data

• A is 3 times as efficient as B → a = 3b (rates).
• A finishes 60 days earlier than B.

Concept/Approach
If T_B is B's time, then A's time T_A = T_B/3. The difference T_B − T_A = 60 gives T_B, then T_A. Combined rate is 1/T_A + 1/T_B.

Step-by-step calculation
T_B − T = 60, with T = T/3 T − T/3 = (2/3)T = 60 → T = 90 days T = 90/3 = 30 days Combined rate = 1/30 + 1/90 = (3 + 1)/90 = 4/90 = 2/45 Combined time = 1 ÷ (2/45) = 45/2 = 22.5 days

Verification
Difference between 90 and 30 is indeed 60 days; efficiency ratio satisfied (A is 3 times faster).

Common pitfalls

• Assuming A's time is 1/3 of B's (correct) but then adding times instead of rates.

Final Answer
22.5 days