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Franny can type 80 words per minute and Matt can type 60...

This topic has 2 expert replies and 0 member replies

Franny can type 80 words per minute and Matt can type 60...

Post Mon Mar 26, 2018 4:54 am
Franny can type 80 words per minute and Matt can type 60 words per minute. If the two together must type up a 14,000-word paper and each person can type for at most 2 hours, what is the least amount of time, in hours, that Matt must type?

A. 2
B. 5/6
C. 11/12
D. 11/9
E. 35/9

The OA is D.

Franny's efficiency = 80 words per minute = 4800 words/h

Matt's efficiency = 60 words per minute = 3600 words/h

Franny completes 9600 words in 2 hours and is left with 4400 words for Matt to complete.

Matt will complete that in 4400/3600 = 11/9 hours.

Is there another strategic approach to solve this PS question? Can any experts help, please? Thanks.

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ErikaPrepScholar Legendary Member
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Post Mon Mar 26, 2018 10:49 am
We could also approach using dimensional analysis.

Franny:
$$2\ hours\ \left(\frac{60\ \min}{1\ hour}\right)\left(\frac{80\ words}{1\ \min}\right)=9600\ words$$

Matt:
$$14000\ words\ -\ 9600\ words\ =\ 4400\ words$$
$$4400\ words\ \left(\frac{1\ \min}{60\ words}\right)\left(\frac{1\ hour}{60\ \min}\right)=\frac{11}{9}hours$$

This is the same process you used, just slightly reordered and slightly more efficient.

We can also eliminate E right off the bat because 35/9 is greater than 2, which violates the rule that each person can type for at most two hours.

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Post Wed Mar 28, 2018 10:16 am
AAPL wrote:
Franny can type 80 words per minute and Matt can type 60 words per minute. If the two together must type up a 14,000-word paper and each person can type for at most 2 hours, what is the least amount of time, in hours, that Matt must type?

A. 2
B. 5/6
C. 11/12
D. 11/9
E. 35/9
We are given that Franny can type 80 words per minute or 80 x 60 = 4800 words per hour. To minimize the amount of time Matt must type, we must maximize the amount of type Franny types, which is 2 hours. If she types for 2 hours (the maximum she can type), then she will have typed 4800 x 2 = 9600 words. Thus, there are 14,000 - 9600 = 4,400 words remaining for Matt to type.

Since Matt can type at a rate of 60 words per minute, or 60 x 60 = 3600 words per hour, the time he will have to spend typing is:

4,400/3,600 = 44/36 = 11/9 hours

Answer: D

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Scott Woodbury-Stewart Founder and CEO

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