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# Rachel needs to type up her 1950-word paper by its 5 pm deadline. If

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Math Expert
Joined: 02 Sep 2009
Posts: 46280
Rachel needs to type up her 1950-word paper by its 5 pm deadline. If [#permalink]

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21 Apr 2017, 07:44
1
8
00:00

Difficulty:

65% (hard)

Question Stats:

52% (02:16) correct 48% (02:33) wrong based on 95 sessions

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Rachel needs to type up her 1950-word paper by its 5 pm deadline. If she starts at least two hours in advance, her typing speed will be a constant 20 words per minute, but for every two minutes beyond 3 pm that she waits before starting, her constant typing speed will increase by one word per minute. What is the latest time at which Rachel can begin typing in order to finish her paper by the deadline?

A. 2:50 pm
B. 3:23 pm
C. 3:30 pm
D. 4:30 pm
E. 4:42 pm

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Re: Rachel needs to type up her 1950-word paper by its 5 pm deadline. If [#permalink]

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21 Apr 2017, 10:40
1
Her constant typing speed at 3PM = 20 words/minute

For every two minute delay after 3 PM constant typing speed increased by 1 word

So if she starts at 3:02 PM her speed will be 21 words/minute

So if she starts at 3:22 PM her speed will be 31 words/minute

So if she starts at 3:30 PM her speed will be 35 words/minute

So if she starts at 4:00 PM her speed will be 50 words/minute

So if she starts at 4:30 PM her speed will be 65 words/minute

So if she starts at 4:42 PM her speed will be 70 words/minute

Going by options,

Option E: if she starts at 4:42 PM with a constant speed of 70 words/minute, she will have 18 minutes to complete. So 1950/70 should be less than equal to 18. But 1950/70 comes to 27.9 minutes. So Option E is ruled out.

Option D: if she starts at 4:30 PM with a constant speed of 65 words/minute, she will have 30 minutes to complete. So 1950/65 should be less than equal to 30. 1950/65 comes to 30 minutes. So Option D is the correct choice.

VP
Joined: 07 Dec 2014
Posts: 1019
Rachel needs to type up her 1950-word paper by its 5 pm deadline. If [#permalink]

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21 Apr 2017, 16:24
Bunuel wrote:
Rachel needs to type up her 1950-word paper by its 5 pm deadline. If she starts at least two hours in advance, her typing speed will be a constant 20 words per minute, but for every two minutes beyond 3 pm that she waits before starting, her constant typing speed will increase by one word per minute. What is the latest time at which Rachel can begin typing in order to finish her paper by the deadline?

A. 2:50 pm
B. 3:23 pm
C. 3:30 pm
D. 4:30 pm
E. 4:42 pm

let m=minimum minutes before 5pm needed by Rachel
m[20+1/2*(120-m)]=1950
m^2-160m+3900=0
(m-30)(m-130)=0
m=30 minutes
5pm-30 minutes=4:30pm
D
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Location: Malaysia
Rachel needs to type up her 1950-word paper by its 5 pm deadline. If [#permalink]

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06 May 2017, 18:16
1
Bunuel wrote:
Rachel needs to type up her 1950-word paper by its 5 pm deadline. If she starts at least two hours in advance, her typing speed will be a constant 20 words per minute, but for every two minutes beyond 3 pm that she waits before starting, her constant typing speed will increase by one word per minute. What is the latest time at which Rachel can begin typing in order to finish her paper by the deadline?

A. 2:50 pm
B. 3:23 pm
C. 3:30 pm
D. 4:30 pm
E. 4:42 pm

OFFICIAL EXPLANATION

Back-solving is a good option for this problem. It is best to begin by checking the last time and then work backwards, since we want the latest time at which Rachel can start.

Starting at 4:42 pm would give Rachel 18 minutes to write at a rate of $$20+\frac{102}{2}=71$$ words per minute. This is approximately 20∗70=1400 words, which is well short of the 1950 necessary to complete the assignment.

Starting at 4:30 pm would give Rachel 30 minutes to write at a rate of $$20+\frac{90}{2}=65$$ words per minute. This is 30∗65=1950 words. Perfect. This must be the correct answer. D.

Could someone help to explain the rate in this problem? constant typing speed will increase by one word per minute.
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Re: Rachel needs to type up her 1950-word paper by its 5 pm deadline. If [#permalink]

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12 Jan 2018, 14:20
Hi All,

This question can be solved by TESTing THE ANSWERS.

This is essentially a rate question, but the rate (and the time spent at that rate) changes depending on what time Rachel begins typing.

Based on the information in the prompt, we know that if Rachel begins typing at 3pm, then she can type for up to 2 hours (re: 120 minutes) at 20 words/minute. Thus, she could type (20)(120) = 2400 total words during that time... and that would be enough time to complete the 1950 word paper. For every TWO minutes past 3pm that she gets started, her typing speed will increase by 1 word/minute (BUT keep in mind that her available typing time will decrease by 2 minutes).

For example, if she begins at 3:02pm, then she can type of up to 118 minutes at 21 words per minute, which would total (21)(118) = 2478 total words.

We're asked for the LATEST that she could begin typing and still complete the paper on time.

Let's TEST Answer E: 4:42pm --> 18 minutes at 71 words/minute = 1,278 total words. That is NOT enough. Eliminate Answer E.

Let's TEST Answer D: 4:30pm --> 30 minutes at 65 words/minute = 1,950 total words. That IS exactly enough, so this must be the answer.

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Joined: 28 Mar 2017
Posts: 5
Rachel needs to type up her 1950-word paper by its 5 pm deadline. If [#permalink]

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13 Jan 2018, 02:18
Hi everyone,

In my opinion, to make an equation is the easiest way to solve this problem.
x - additional speed for every 2 minutes, after 3 pm
(120-2x) - time left for writing
(20+x) - speed
The equation is the following:
(120-2x)(20+x)=1950
x^2-40x+450=0
x=45
Meaning that she can start writing 45*2=90 min after 3pm, or, in other words, 4:30pm.
ANS: D

Rachel needs to type up her 1950-word paper by its 5 pm deadline. If   [#permalink] 13 Jan 2018, 02:18
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