(Question) Translating English into Fractions

[STI-R]

Hey folks,
I'm having a hard time trying to put the following statement together into numbers. If there are 18 rooms in the house that needs to be cleaned how do I find out nick's rate? Could someone try to explain it to me like I'm five years old? I'm most confused by "third of the time it takes nick to clean the entire house alone" I already know how to add rates and the answer to this problem. I just want a clear explanation to translating the English into numbers.

"Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone."

Here is the full problem for anyone curious.
Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

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Hi STI-R,

GMAT Quant questions sometimes give you information "out of order" to see if you can organize the data efficiently.

Here, we're told that Manuel can clean an entire house in 6 hours.

We're going to use THAT information to properly translate the PRIOR sentence: "Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone."

Since Manuel cleans the whole house in 6 hours, he cleans HALF the house in HALF the time: 3 hours.

So, 3 = (1/3)(N)

9 = N

Nick's time to clean the entire house = 9 hours

With both Manuel's time (6 hours) and Nick's time (9 hours), you can then use the Work Formula to figure out how long it takes the two of them to clean the entire house, when working together:

(6x9)/(6+9) = 54/15 = 18/5 = 3.6 hours

GMAT assassins aren't born, they're made,
Rich

[STI-R]

Thank you so much for the explanation. I'm very weak at translating these so called "out of order" problems. Is there anything that you can recommend me to help me become better at problems like this?

Hi STI-R,

GMAT Quant questions sometimes give you information "out of order" to see if you can organize the data efficiently.

Here, we're told that Manuel can clean an entire house in 6 hours.

We're going to use THAT information to properly translate the PRIOR sentence: "Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone."

Since Manuel cleans the whole house in 6 hours, he cleans HALF the house in HALF the time: 3 hours.

So, 3 = (1/3)(N)

9 = N

Nick's time to clean the entire house = 9 hours

With both Manuel's time (6 hours) and Nick's time (9 hours), you can then use the Work Formula to figure out how long it takes the two of them to clean the entire house, when working together:

(6x9)/(6+9) = 54/15 = 18/5 = 3.6 hours

GMAT assassins aren't born, they're made,
Rich

[[email protected]]

Hi STI-R,

There are plenty of great sources for practice problems (all of the GMAC material, for example), but I think you're looking for more of a tactic or philosophy.

As I read Quant questions, I make it a point to take lots of notes. I'll write down variables and numbers, but I always make sure to LABEL my work. As long as I understand what everything means, then I shouldn't get "lost" in a question.

When I come across something that's easy to deal with, then I'll stop and deal with it. For example, consider what you could do with the following information:

"The average of two integers is 50"

This might seem like a minor piece of information, but look how quickly you can deal with it....

X, Y = integers
(X+Y)/2 = 50
X+Y = 100

With these notes now "out of the way", I can move on with the rest of the question and refer back to this information as needed.

Sometimes the first piece of information is "easy", sometimes the first piece is "tougher", but the second piece of information is "easy" (as in this work formula question). If you don't understand something that you read, then look for easy things to deal with first, then incorporate the tougher stuff after.

GMAT assassins aren't born, they're made,
Rich

[GMATinsight]

Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together?

A. 1.5
B. 2
C. 2.4
D. 3
E. 3.6

Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone

i.e. Manuel finishes cleaning FULL house in TWO third of the time it takes Nick to clean the entire house alone

i.e. M = (3/2)N where M and N are efficiencies of Manuel and Nick

Time taken by M to clean House = 6 hours
i.e. Time taken by N to clean House = (3/2)*6 = 9 hours

1 Hour work of both M and N working together = (1/6)+(1/9) = (3+2)/18 = 5/18

5/18 House is cleaned by them together in 1 hours
Full House will be cleaned by them together in 1/(5/18) = 18/5 = 3.6 hours

Answer: option E