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M07-03

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M07-03 [#permalink]

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Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, approximately how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

A. 41.4
B. 34.1
C. 13.4
D. 12.4
E. 10.8
[Reveal] Spoiler: OA

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New post 16 Sep 2014, 00:34
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Official Solution:

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, approximately how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

A. 41.4
B. 34.1
C. 13.4
D. 12.4
E. 10.8


Break down the problem into two pieces: typing and editing.

"Mary needs 30 hours to type the report": Mary's typing rate \(= \frac{1}{30}\) job/hour;

"Mary and Jim can type up a report in 12.5": \(\frac{1}{30} + \frac{1}{x}= \frac{1}{12.5}=\frac{2}{25}\), where \(x\) is the time needed for Jim to type the report alone. Solving gives \(x=\frac{150}{7}\);

"Jim needs 12 hours to edit the report": Jim's editing rate \(= \frac{1}{12}\) job/hour;

"Mary and Jim can edit a report in 7.5": \(\frac{1}{y}+\frac{1}{12}=\frac{1}{7.5}=\frac{2}{15}\), where \(y\) is the time needed for Mary to edit the report alone. Solving gives \(y=20\);

"How many hours will it take if Jim types the report and Mary edits it immediately after he is done": \(x+y= \frac{150}{7}+20 \approx 41.4\)


Answer: A
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Re: M07-03 [#permalink]

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New post 12 Oct 2014, 15:16
Most of the work/rate problems are causing trouble to me. Is there any thread dedicated to breaking down the common types and tricks, dealing with work/rate problems.

Something Similar to the distance speed time one: distance-speed-time-word-problems-made-easy-87481.html

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earnit wrote:
Most of the work/rate problems are causing trouble to me. Is there any thread dedicated to breaking down the common types and tricks, dealing with work/rate problems.

Something Similar to the distance speed time one: distance-speed-time-word-problems-made-easy-87481.html


Theory on work/rate problems: work-word-problems-made-easy-87357.html

All DS work/rate problems to practice: search.php?search_id=tag&tag_id=46
All PS work/rate problems to practice: search.php?search_id=tag&tag_id=66
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Collection of Questions:
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Re: M07-03 [#permalink]

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New post 24 Feb 2015, 05:31
Bunuel wrote:
Official Solution:

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, approximately how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

A. 41.4
B. 34.1
C. 13.4
D. 12.4
E. 10.8


Break down the problem into two pieces: typing and editing.

"Mary needs 30 hours to type the report": Mary's typing rate \(= \frac{1}{30}\) job/hour;

"Mary and Jim can type up a report in 12.5": \(\frac{1}{30} + \frac{1}{x}= \frac{1}{12.5}=\frac{2}{25}\), where \(x\) is the time needed for Jim to type the report alone. Solving gives \(x=\frac{150}{7}\);

"Jim needs 12 hours to edit the report": Jim's editing rate \(= \frac{1}{12}\) job/hour;

"Mary and Jim can edit a report in 7.5": \(\frac{1}{y}+\frac{1}{12}=\frac{1}{7.5}=\frac{2}{15}\), where \(y\) is the time needed for Mary to edit the report alone. Solving gives \(y=20\);

"How many hours will it take if Jim types the report and Mary edits it immediately after he is done": \(x+y= \frac{150}{7}+20 \approx 41.4\)


Answer: A


My approach is the same except that in the end, i calculate the combined Rate for Mary and Jim after having found their new rates of editing and typing respectively.

So that in the end, the time taken would be the reciprocal of the Total Rate. But then with this approach my answer changes.

Please tell me what am i doing wrong here?

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Re: M07-03 [#permalink]

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New post 24 Feb 2015, 06:03
earnit wrote:
Bunuel wrote:
Official Solution:

Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, approximately how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

A. 41.4
B. 34.1
C. 13.4
D. 12.4
E. 10.8


Break down the problem into two pieces: typing and editing.

"Mary needs 30 hours to type the report": Mary's typing rate \(= \frac{1}{30}\) job/hour;

"Mary and Jim can type up a report in 12.5": \(\frac{1}{30} + \frac{1}{x}= \frac{1}{12.5}=\frac{2}{25}\), where \(x\) is the time needed for Jim to type the report alone. Solving gives \(x=\frac{150}{7}\);

"Jim needs 12 hours to edit the report": Jim's editing rate \(= \frac{1}{12}\) job/hour;

"Mary and Jim can edit a report in 7.5": \(\frac{1}{y}+\frac{1}{12}=\frac{1}{7.5}=\frac{2}{15}\), where \(y\) is the time needed for Mary to edit the report alone. Solving gives \(y=20\);

"How many hours will it take if Jim types the report and Mary edits it immediately after he is done": \(x+y= \frac{150}{7}+20 \approx 41.4\)


Answer: A


My approach is the same except that in the end, i calculate the combined Rate for Mary and Jim after having found their new rates of editing and typing respectively.

So that in the end, the time taken would be the reciprocal of the Total Rate. But then with this approach my answer changes.

Please tell me what am i doing wrong here?


The point is that typing and editing are two separate actions: Jim types the report and Mary edits it immediately after he is done. Hence you cannot use combined rate for those two actions.

Hope it's clear.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M07-03 [#permalink]

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New post 03 May 2016, 13:14
Bunuel wrote:

"Jim needs 12 hours to edit the report": Jim's editing rate \(= \frac{1}{12}\) job/hour;

"Mary and Jim can edit a report in 7.5": \(\frac{1}{y}+\frac{1}{12}=\frac{1}{7.5}=\frac{2}{15}\), where \(y\) is the time needed for Mary to edit the report alone. Solving gives \(y=20\);


Can someone please break this out by step? I got here (as well the other step before this that is the same style of equation) during the problem but I got stuck proceeding on the math. Am I supposed to find the LCM for 7.5 and 12, add them then cross multiply? Do I just have to multiply 12 by 7.5 to quickly come up with a workable denominator?
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Re: M07-03 [#permalink]

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New post 04 May 2016, 06:54
redfield wrote:
Bunuel wrote:

"Jim needs 12 hours to edit the report": Jim's editing rate \(= \frac{1}{12}\) job/hour;

"Mary and Jim can edit a report in 7.5": \(\frac{1}{y}+\frac{1}{12}=\frac{1}{7.5}=\frac{2}{15}\), where \(y\) is the time needed for Mary to edit the report alone. Solving gives \(y=20\);


Can someone please break this out by step? I got here (as well the other step before this that is the same style of equation) during the problem but I got stuck proceeding on the math. Am I supposed to find the LCM for 7.5 and 12, add them then cross multiply? Do I just have to multiply 12 by 7.5 to quickly come up with a workable denominator?


\(\frac{1}{y}+\frac{1}{12}=\frac{1}{7.5}=\frac{2}{15}\)

\(\frac{1}{y}=\frac{2}{15}-\frac{1}{12}=\frac{8}{60}-\frac{5}{60}=\frac{3}{60}=\frac{1}{20}\)
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M07-03 [#permalink]

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New post 23 Sep 2017, 08:28
I think the part "immediately after he is done" is the key to answer this question. It means they are not working simultaneously.

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Re: M07-03   [#permalink] 23 Sep 2017, 08:28
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