Final answer:
To find how long B will take to work alone, we calculate the work rates of A and B. B's work rate is 1/x and A's is 2/3x. Together, their combined work rate is 1/18, which gives us the equation 5/3x = 1/18. Solving for x gives us 30 days, so B will take 30 days to complete the work alone. Option C is the correct answer.
Step-by-step explanation:
The question requires solving a work rate problem to determine how long it will take for B to complete the work alone. A takes 50% more time than B to complete the same work. To find the time B takes to complete the work alone, we need to understand the concept of work rates and how they combine when two agents are working together.
Let's assume B takes 'x' days to complete the work. This means A takes '1.5x' days (50% more than B). If B does 1 job in 'x' days, B's work rate is 1/x jobs per day. Similarly, A's work rate is 1/1.5x or 2/3x jobs per day.
When A and B work together their work rates add up. So, the combined work rate is 1/x + 2/3x = (3+2)/3x = 5/3x jobs per day. Since together they take 18 days to complete the work, we can equate the combined work rate to 1/18 (because they complete 1 job in 18 days).
Setting up the equation: 5/3x = 1/18. Solving for 'x' we get: x = 5/3 * 18 = 30 days. Therefore, B would take 30 days to complete the work on his own.
The correct answer is Option c) 30 days.