Problema Solution
An experienced accountant can balance the book twice as fast as a new accountant. Working together it takes the accountant 8 hours. How long would it take the experienced accountant working alone?
Answer provided by our tutors
Let the time of the new accountant be 2x, and the time of the experienced accountant be x.
Since it take the new accountant 2x hours to finish the whole job, it takes 1 hours to finish 1/2x of the job. So does this apply to the experienced accountant.
We have
1/(1/x + 1/2x) = 8 or
1/[3/(2x)] = 8 or
2x/3 = 8 or
2x = 24 or
x = 12 hours.
Another way to do this is to think like this:
the new accountant finishs the whole job in 2x hours; the experienced accountant finishs the whole job in x hours, and he also finishs 2 whole jobs in 2x hours.
In 2x hours, they contribute a total of 3 whole jobs, and they finish 1 whole job in 2x/3 hours if they are working together.
2x/3 = 8
2x = 24
x = 12 hours.