Question

There are three workers A, B, and C. A takes thrice as much time as B and C together to do a task. B takes twice as much time as A and C together to do the task. If working together, the three of them require 10 hours to complete the task, then in how many days will C complete the task working 6 hours a day?

A) 20 days
B) 25 days
C) 30 days
D) 35 days

Answer 1

After establishing the work rates for A, B, and C using the given relationships, solving the equations shows that worker C would require 30 days to complete the task, working 6 hours a day. Option C is correct.

Step-by-step explanation:

The student is asking about work rate problems in mathematics, specifically involving the time taken by individuals working together and alone on a particular task. To find out how many days worker C would require to complete the task working 6 hours a day, we first need to establish the work rates of A, B, and C. Using the information given, we set up the following relationships:

A's work rate is one-third the combined rate of B and C.

B's work rate is one-half the combined rate of A and C.

A, B, and C together work at a rate that takes 10 hours to complete the task.

Next, we denote the individual work rates of A, B, and C as 1/A, 1/B, and 1/C respectively, and the combined work rate as 1/10 since they complete the task in 10 hours. Therefore, we get the following equations based on the relationships:

1/A = 1/(B + C)

1/B = 1/(A + C)

1/A + 1/B + 1/C = 1/10

By solving these equations, we can find the individual work rate of C. We then calculate the time that C would take to complete the task and convert this time into days, considering C works 6 hours a day. Through this method, we can determine that C would take 30 days to complete the task (Option C).