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Source: — Problem Solving |
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by theCodeToGMAT » Mon Jan 27, 2014 7:28 pm
Cellphone = 14 min
Rate = 1/14*60

Laptop = 14 sec
Rate = 1/14

Combined(1/t): 1/14*60 + 1/14 = 1/14 ( 61/60)

So, t = 14 * 60/61

that would result in a touch lower result than 14.

[spoiler]{D}[/spoiler]
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by GMATGuruNY » Mon Jan 27, 2014 9:07 pm
The problem above is the equivalent of the following:
Adam can complete a certain job in 14 minutes. Bob can complete this same job in 14 seconds. If Adam and Bob work together at their respective rates, approximately how many seconds will it take them to complete the job?

7.17
9.12
11.44
13.77
14
Let the job = 14 units.
Since Adam takes 14 minutes to complete the job, Adam's rate = w/t = 14/14 = 1 unit per minute.
Since Bob takes 14/60 of a minute to complete the job, Bob's rate = w/t = 14/(14/60) = 60 units per minute.
Time for Adam and Bob working together = w/(combined rate) = 14/(1+60) = 14/61 of a minute.
Since 14/60 of a minute = 14 seconds -- and 14/61 is LESS than 14/60 -- the time for Adam and Bob together must be just a bit less than 14 seconds.

The correct answer is D.
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by [email protected] » Tue Jan 28, 2014 2:35 pm
Hi shibsriz,

Both Rahul and Mitch have presented solutions that convert the data into rates or units. Here's another way to approach this question: the Work Formula.

Since we have 2 devices performing the same task and we're asked how long it would take them, working together, to do the task, we can use:

(AxB)/(A+B)

We have to make sure that we use the same units for each variable.
A = 14 seconds
B = 14 minutes = 14(60) = 840 seconds

Now, plug in...
(14x840) / (14+840) = (14x840) / (854)

Now simplify (either in steps or all at once)

(14x840)/854 = (7x840)/427 = 840/61 = a little less than 14

Final Answer: D

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