The formula for solving these equations is:

1/X + 1/Y = 1/Together

Where X is the time it takes for machine X to finish, Y is the time it takes for machine Y to finish and Together is the time both can finish together.

Here is what we know. Machine X can finish alone in 9 hours. It worked 3 hours by itself, so it finished 1/3 of the job (3 hours/9 hours) by itself. Then it worked the final 4 hours finishing the job with Machine Y. So to finish the remaining 2/3 of the job, we know that Machine X would take 6 hours to do it, and both together would take 4 hours to do it. Plugging into the formula we can find that:

1/6 + 1/Y = 1/4

Simplifying down, Y = 12. However, this is the amount of time it would take for Y to finish 2/3 of the work. So dividing 12 by 2/3, we can find out how long it would take Y to finish all of the work:

12/(2/3) = 18 hours

The answer is A

My favorite way to do these problems is to assign a value to the job.

Let's say that the job is to make 18 pizzas. Machine X can make 18 pizzas (the whole job) in 9 hours, or 2 pizzas per hour.

If Machine X worked on the job alone for 3 hours, it would have made 6 pizzas. So, we need 12 more pizzas to finish the job.

It took both machines, together, 4 hours to make 12 pizzas (to finish the job), or 3 pizzas per hour. Since Machine X makes 2 pizzas per hour, Machine Y must make 1 pizza per hour.

Since Machine Y makes 1 pizza per hour, it would take 18 hours to do the entire job (making 18 pizzas).

Hope this helps!

I get everything. Can you just explain the last step

"12/(2/3) = 18 hours"

Thanks.

Isn't the answer C here?

mim,

I, too, got that answer. But I think that you and I are doing something wrong.

Here is what I did, maybe it can help you out....

x completes the job in 9 hrs

x completes 1/3 of the job in 3 hours.

2/3 of the job is completed in 4 hours by X and Y

working together to complete 3/3 of the job will take X and Y 6hrs (4 x 3/2)..

we already know that x can complete 1/9 of the job in an hour; working together they can complete 1/6 of the job in an hr....to find out what y can complete in an hour

1/9 + 1/y = 1/6

using a common factor of 18....2/18 +1/18 = 3/18...

since y can complete 1/18 of the job in an hour, would take 18 hours to complete the whole task. The answer is A....hope that helps.

mim3 wrote:Isn't the answer C here?

(C) (and (d) and (e) for that matter) just don't make sense on this question.

By itself, it would take X 6 hours to finish the remaining 2/3 of the job. If Y worked at the same speed as X, then together it would take X and Y half that time, i.e. 3 hours. Since it takes X and Y MORE than 1/2 the time it would take X alone, Y must be a slower worker than X: eliminate (c), (d) and (e).

Cappy and VP_Jim both posted great ways to actually solve this problem. If you get stuck on the actual solution for work problems, you can often use some logic and common sense to eliminate 2-4 choices.