Final answer:
Worker A is twice as fast as B and finishes 30 days earlier than B, who would take 60 days. When working together, their combined work rate allows them to complete the job in 20 days. The correct choice is (c) 20 days.
Step-by-step explanation:
The question at hand involves calculating the time it would take for two workers, A and B, with different work rates to complete a job together. Given that worker A is twice as fast as worker B, we first need to establish the relationship between their rates of work.
Let's assume that worker B can finish the work in 'x' days. Consequently, worker A, being twice as fast, would complete the same job in 'x/2' days. It is given that worker A finishes the work 30 days earlier than B, which allows us to write the equation x/2 = x - 30. Solving for 'x' gives us the number of days worker B would need to complete the job solo, which turns out to be 60 days.
Next, we calculate the work rates for A and B. Worker A completes 1/30 of the work per day, while worker B completes 1/60 of the work per day. When both work together, we add their work rates to determine the combined work rate. This gives us (1/30 + 1/60) of the work per day. Common denominator for 30 and 60 is 60, so the combined rate simplifies to (2/60 + 1/60), or 3/60, which reduces to 1/20. Therefore, working together, workers A and B can complete the job in 20 days.
The correct option, in this case, is choice (c) 20 days.