Question

A and B can do a job together in 25 days. After 15 days of working together, B leaves. If they complete the remaining part of the job in 20 days, how long would it take to complete the job working separately?

Answer 1

A and B each have a work rate of 1/50 job/day, meaning it would take each of them 50 days to complete the job individually.

Step-by-step explanation:

Let us assign work rates to A and B where the amount of work done is represented by the fraction of the job completed per day. If A and B together finish the job in 25 days, their combined work rate is 1 job per 25 days or 1/25 job/day. After working for 15 days together, they complete 15/25 (or 3/5) of the job. Since they need 20 more days to finish the rest (2/5 of the job), we can determine A's individual work rate.

Since A alone requires 20 days to finish 2/5 of the job, A's work rate is 2/5 job per 20 days, which reduces to 1/50 job/day. To find B's work rate, we subtract A's rate from their combined rate: 1/25 - 1/50 = 1/50 job/day. This means B also has a work rate of 1/50 job/day. Therefore, it would take A or B 50 days to complete the job individually.