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jamesk486: Master | Next Rank: 500 Posts; Posts: 141; Joined: Wed Mar 28, 2007 9:24 pmFollowed by: 1 member; Thanked: 2 times

by jamesk486 » Wed Jul 09, 2008 10:27 pm

Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y, working alone, to complete the entire job?

(A) 18 (B)13+1/2 (C)7+1/5 (D)4+1/2 (E)3+2/3

i always get so confused!

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Source: Beat The GMAT — Problem Solving | Wed Jul 09, 2008 10:27 pm

CappyAA: Master | Next Rank: 500 Posts; Posts: 124; Joined: Mon Jun 16, 2008 11:07 amFollowed by: 14 members; Thanked: 21 times; GMAT Score:750

by CappyAA » Wed Jul 09, 2008 10:47 pm

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

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VP_Jim: GMAT Instructor; Posts: 1223; Joined: Thu May 01, 2008 3:29 pmFollowed by: 15 members; Location: Los Angeles, CA; Thanked: 185 times

by VP_Jim » Thu Jul 10, 2008 12:37 am

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!

Jim S. | GMAT Instructor | Veritas Prep

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AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

by AleksandrM » Thu Jul 10, 2008 9:33 am

I get everything. Can you just explain the last step

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

Thanks.

https://second-lap.blocked/

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mim3: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Fri Apr 04, 2008 12:36 pm; Thanked: 4 times; GMAT Score:680

by mim3 » Thu Jul 10, 2008 11:24 am

Isn't the answer C here?

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AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

by AleksandrM » Thu Jul 10, 2008 4:07 pm

mim,

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

https://second-lap.blocked/

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lordpapi63: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sun Jun 15, 2008 10:19 pm

by lordpapi63 » Thu Jul 10, 2008 5:38 pm

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.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Fri Jul 11, 2008 8:55 am

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.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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