Final answer:
To find the time required for A to complete the whole job when working alone, we need to understand the work done by A and B together and B alone. When A and B work together for 4 hours, they complete 100% of the work. When B works alone for 4 hours, he completes 25% of the work. A's work rate alone is 18.75% per hour. Therefore, it will take A approximately 5.33 hours to complete the whole job when working alone.
Step-by-step explanation:
To find the time required for A to complete the whole job when working alone, we need to understand the work done by A and B together and B alone.
Let's assume the total time required to complete the job is T hours.
When A and B work together for 4 hours, they complete 100% of the work. So, the work done by A and B together is 100% of the job.
When B works alone for 4 hours, he completes 25% of the work. So, the work done by B alone is 25% of the job.
Since A and B complete 100% of the job together in 4 hours, we can say that their combined work rate is 100%/4 = 25% per hour.
Now, if B completes 25% of the job alone in 4 hours, his work rate is 25%/4 = 6.25% per hour.
Since A and B's combined work rate is 25% per hour and B's work rate alone is 6.25% per hour, A's work rate alone must be 25% - 6.25% = 18.75% per hour.
To find the time required for A to complete the whole job when working alone, we can set up the equation:
A's work rate alone * Time taken by A = 100% (the whole job).
18.75% * Time taken by A = 100%
Time taken by A = 100% / 18.75% = 5.33 hours.