A would have taken 12 hours less than what B would have taken to complete a task if each of them worked alone. Working together they can complete the task in 17.5 hours. How many hours B alone can do the work?Options36424432

Let's denote the time it would take for B to complete the task alone as x hours.

According to the problem, A would take (x - 12) hours to complete the task alone.

The rate of work done by A is 1/(x - 12) tasks per hour, and the rate of work done by B is 1/x tasks per hour.

When A and B work together, they can complete the task in 17.5 hours, so their combined rate of work is 1/17.5 tasks per hour.

Therefore, we can set up the equation:

1/(x - 12) + 1/x = 1/17.5

To solve this equation, we first multiply each term by 17.5x(x - 12) to get rid of the fractions:

17.5x + 17.5(x - 12) = x(x - 12)

Expanding and simplifying gives:

17.5x + 17.5x - 210 = x^2 - 12x

35x - 210 = x^2 - 12x

Rearranging terms gives:

x^2 - 47x + 210 = 0

This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve it using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a):

x = [47 ± sqrt((47)^2 - 41210)] / (2*1)

x = [47 ± sqrt(2209 - 840)] / 2

x = [47 ± sqrt(1369)] / 2

x = [47 ± 37] / 2

The two possible solutions are x = 42 and x = 5. However, since A would take 12 hours less than B to complete the task, B cannot take 5 hours, so we discard this solution.

Therefore, B alone can do the work in 42 hours. So, the correct option is 42.