Select the correct answerA 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?Options42364432
Question
Select the correct answerA 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?Options42364432
Solution
Let's denote the time it would take for B to complete the task alone as T.
According to the problem, A would take (T - 12) hours to complete the task alone.
The rate at which A completes the task is 1/(T - 12) tasks per hour, and the rate at which B completes the task is 1/T tasks per hour.
When A and B work together, they can complete the task in 17.5 hours, so their combined rate is 1/17.5 tasks per hour.
We can set up the equation:
1/(T - 12) + 1/T = 1/17.5
To solve this equation, we can multiply every term by T*(T - 12)*17.5 to get rid of the fractions:
17.5T + 17.5(T - 12) = T*(T - 12)
Expanding and simplifying gives:
35T - 210 = T^2 - 12T
Rearranging terms gives a quadratic equation:
T^2 - 47T + 210 = 0
Factoring this equation gives:
(T - 42)(T - 5) = 0
The solutions to this equation are T = 42 and T = 5.
However, since A would have taken 12 hours less than B to complete the task, T cannot be 5.
Therefore, the time it would take for B to complete the task alone is 42 hours.
So, the correct answer is 42.
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