Question 765260
Let x = the number of hours the first person takes to do the whole job alone.
Let y = the number of hours the second person takes to do the whole job alone.
When they work together it will take them n hours as given by the following formula:
(1) n = 1/(1/x + 1/y)
This is a very useful formula to use on this type of problem, put it in your file for future work.
In your problem we know two facts - just enough to solve for two unknowns, x and y.
Firstly we know that the total time it takes for the two people working together is 6 hours, therefore
(2) n = 6
The second fact is that one of them works twice as fast as the other, so that person takes one half the time as the other. Let's say that x is the faster worker, therefore we have
(3) x = y/2
Now put (2) and (3) into (1) to get
(4) 6 = 1/(2/y + 1/y) or
(5) 6 = y/(2 + 1) or
(6) 6 = y/3 or
(7) y = 18
So it takes the slower person 18 hours to do the job alone, whereas it only takes the faster person one half of this time or 9 hours.
Let's check this using the magic formula (1).
Is (6 = 1/(1/9 + 1/18))?
Is (6 = 1/(3/18))?
Is (6 = 18/3)?
Is (6 = 6)? Yes
Answer: The faster worker takes 9 hours to do the whole job alone.