Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 19 Sep 2010
Posts: 25

It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
07 Oct 2010, 10:49
Question Stats:
58% (02:20) correct 42% (02:38) wrong based on 733 sessions
HideShow timer Statistics
It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages? A. 5 B. 6 C. 8 D. 10 E. 12
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 48037

Re: Hours to type pages
[#permalink]
Show Tags
07 Oct 2010, 11:09
Barkatis wrote: It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages? 5 6 8 10 12 Can anyone explain the method to work with such problems ? Cause I always get them wrong ! And if you know any similar questions, please share. Thanks Let the time needed for Jack to type 20 pages by \(j\) hours, then for Tom it would be \(j2\) hours. So the rate of Jack is \(rate=\frac{job}{time}=\frac{20}{j}\) pages per hour and the rate of Tom \(rate=\frac{job}{time}=\frac{20}{j2}\) pages per hour. Their combined rate would be \(\frac{20}{j}+\frac{20}{j2}\) pages per hour and this equal to \(\frac{25}{3}\) pages per hour > \(\frac{20}{j}+\frac{20}{j2}=\frac{25}{3}\) > \(\frac{60}{j}+\frac{60}{j2}=25\). At this point we can either try to substitute the values from the answer choices or solve quadratic equation. Remember as we are asked to find time needed for Jack to type \(40\) pages, then the answer would be \(2j\) (as \(j\) is the time needed to type \(20\) pages). Answer E works: \(2j=12\) > \(j=6\) > \(\frac{60}{6}+\frac{60}{62}=10+15=25\). Answer: E. Some work problems with solutions: timenworkproblem82718.html?hilit=reciprocal%20ratefacingproblemwiththisquestion91187.html?highlight=rate+reciprocalwhatamidoingwrongtobunuel91124.html?highlight=rate+reciprocalgmatprepps93365.html?hilit=reciprocal%20ratequestionsfromgmatpreppracticeexampleasehelp93632.html?hilit=reciprocal%20rateagoodone98479.html?hilit=ratesolutionrequired100221.html?hilit=work%20rate%20doneworkproblem98599.html?hilit=work%20rate%20doneHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8196
Location: Pune, India

Re: Hours to type pages
[#permalink]
Show Tags
06 Jan 2012, 03:29
Barkatis wrote: It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages? 5 6 8 10 12 Can anyone explain the method to work with such problems ? Cause I always get them wrong ! And if you know any similar questions, please share. Thanks You can solve equations like the one given below using some logic. Even if you do not have options, you can still get your answer very easily. You don't really need to make a quadratic. \(\frac{20}{t} + \frac{20}{(t+2)} = \frac{25}{3}\) Look at the right hand side of the equation. The fraction is in the lowest form. So you looking for a 3 somewhere in the denominator. Also note that 25/3 is a little more than 8. Can 't' be 3? No, because 20/3 + 20/5 is a little more than 10. Can 't+2' be 3? No, because then t = 1 and the sum on the left hand side will be more than 20. Can 't+2' be 6 instead? 20/4 + 20/6 = 25/3 So t must be 4 and t+2 must be 6.
_________________
Karishma Veritas Prep GMAT Instructor
Save up to $1,000 on GMAT prep through 8/20! Learn more here >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Manager
Joined: 06 May 2012
Posts: 67

Re: Hours to type pages
[#permalink]
Show Tags
10 Nov 2012, 15:03
Bunuel wrote: Let the time needed for Jack to type 20 pages by \(j\) hours, then for Tom it would be \(j2\) hours. So the rate of Jack is \(rate=\frac{job}{time}=\frac{20}{j}\) pages per hour and the rate of Tom \(rate=\frac{job}{time}=\frac{20}{j2}\) pages per hour.
Their combined rate would be \(\frac{20}{j}+\frac{20}{j2}\) pages per hour and this equal to \(\frac{25}{3}\) pages per hour > \(\frac{20}{j}+\frac{20}{j2}=\frac{25}{3}\) > \(\frac{60}{j}+\frac{60}{j2}=25\). At this point we can either try to substitute the values from the answer choices or solve quadratic equation. Remember as we are asked to find time needed for Jack to type \(40\) pages, then the answer would be \(2j\) (as \(j\) is the time needed to type \(20\) pages). Answer E works: \(2j=12\) > \(j=6\) > \(\frac{60}{6}+\frac{60}{62}=10+15=25\). Bunuel, can you explain how below is possible? Combined 20 pg and equaled to 25 pg? Their combined rate would be \(\frac{20}{j}+\frac{20}{j2}\) pages per hour and this equal to \(\frac{25}{3}\) pages per hour > \(\frac{20}{j}+\frac{20}{j2}=\frac{25}{3}\)



Math Expert
Joined: 02 Sep 2009
Posts: 48037

Re: Hours to type pages
[#permalink]
Show Tags
12 Nov 2012, 09:41
gmatchase wrote: Bunuel wrote: Let the time needed for Jack to type 20 pages by \(j\) hours, then for Tom it would be \(j2\) hours. So the rate of Jack is \(rate=\frac{job}{time}=\frac{20}{j}\) pages per hour and the rate of Tom \(rate=\frac{job}{time}=\frac{20}{j2}\) pages per hour.
Their combined rate would be \(\frac{20}{j}+\frac{20}{j2}\) pages per hour and this equal to \(\frac{25}{3}\) pages per hour > \(\frac{20}{j}+\frac{20}{j2}=\frac{25}{3}\) > \(\frac{60}{j}+\frac{60}{j2}=25\). At this point we can either try to substitute the values from the answer choices or solve quadratic equation. Remember as we are asked to find time needed for Jack to type \(40\) pages, then the answer would be \(2j\) (as \(j\) is the time needed to type \(20\) pages). Answer E works: \(2j=12\) > \(j=6\) > \(\frac{60}{6}+\frac{60}{62}=10+15=25\). Bunuel, can you explain how below is possible? Combined 20 pg and equaled to 25 pg? Their combined rate would be \(\frac{20}{j}+\frac{20}{j2}\) pages per hour and this equal to \(\frac{25}{3}\) pages per hour > \(\frac{20}{j}+\frac{20}{j2}=\frac{25}{3}\) We are told that "working together, Jack and Tom can type 25 pages in 3 hours", thus their combined rate is 25/3 pages per hour. We also know that Jack's rate is 20/j pages per hour and Tom's rate is 20/(j2) pages per hour, thus their combined rate is 20/j+20/(j2) pages per hour. So, we have that 20/j+20/(j2)=25/3. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 13 Aug 2012
Posts: 441
Concentration: Marketing, Finance
GPA: 3.23

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
13 Nov 2012, 22:44
Time it takes Jack and Tom to print 20 pages: j = t + 2, t = j  2 Rate Equation: 20/j + 20/j2 = 25/3 1/j + 1/j2 = 5/12 What is 2j? Therefore, the answer choices are 2j. A. 5/2 > 2/5 + 2 = 12/5 B. 3 > 1/3 + 1 = 4/3 C. 4 > 1/4 + 1/2 = 3/4 D. 5 > 1/5 + 1/3 = 8/15 E. 6 > 1/6 + 1/4 = 10/24 = 5/12 BINGO! Answer: E
_________________
Impossible is nothing to God.



VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1016
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
12 Feb 2013, 12:44
I was not able to solve the quadratic; 20/j + 20/j+2 = 25/3 I ended up simplifying it to 5x^2  14x  24 = 0 ; I got the value of x as 4 mins and for 40 copies as 8 mins.... can anyone help me , where did i go wrong??????????



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8196
Location: Pune, India

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
12 Feb 2013, 20:10
Archit143 wrote: I was not able to solve the quadratic; 20/j + 20/j+2 = 25/3 I ended up simplifying it to 5x^2  14x  24 = 0 ; I got the value of x as 4 mins and for 40 copies as 8 mins.... can anyone help me , where did i go wrong?????????? You did everything right except the last part of assigning the right variable to the right person. The quadratic you got was 20/j + 20/j+2 = 25/3 Since Jack takes 2 more hrs than Tom, 20/j is the rate of Tom and 20/(j+2) is the rate of Jack. You got j = 4 So j+2 = 6 = Time taken by Jack to type 20 pages So time taken by Jack to type 20 pages = 2*6 = 12 When assigning variables, its always advisable to assign x to the value you need to find i.e. j should have been the time taken by Jack since you need to find Jack's time. Not that it changes the question in any way but you avoid this particular error you committed here. Also, in that case, it is easier to plug in values from the answer choices and you don't really need to solve the quadratic.
_________________
Karishma Veritas Prep GMAT Instructor
Save up to $1,000 on GMAT prep through 8/20! Learn more here >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Manager
Status: Breaking my head!!
Joined: 27 Jan 2013
Posts: 66
Location: India
Concentration: General Management, Operations
GPA: 3.51
WE: Other (Transportation)

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
03 Mar 2013, 02:27
Barkatis wrote: It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages?
A. 5 B. 6 C. 8 D. 10 E. 12 Got stuck in the quadratic. However when i looked a little closely at the question I realized I could work by employing logic. Since the combined rate of work is 25 pages in 3 hours it implies their combined rate is just marginally greater than 8 pages per hour. The question requires us to determine how long Jack takes working alone to type 40 pages. Now since their combined rate is 8 pages an hour working together they would finish 40 pages in about 5 hours. We also know that Jack's rate is slower than Tom's. So if Jack works alone he must take more than double the time it would have taken had they worked together. i.e little more than 10. Only E suffices. P.S. Could anyone let me know if we should follow this approach of using Logic to arrive at the answer if the Work Rate problems become convoluted??(Like involving massive quadratics)



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8196
Location: Pune, India

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
03 Mar 2013, 22:52
Dipankar6435 wrote: Barkatis wrote: It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages?
A. 5 B. 6 C. 8 D. 10 E. 12 Got stuck in the quadratic. However when i looked a little closely at the question I realized I could work by employing logic. Since the combined rate of work is 25 pages in 3 hours it implies their combined rate is just marginally greater than 8 pages per hour. The question requires us to determine how long Jack takes working alone to type 40 pages. Now since their combined rate is 8 pages an hour working together they would finish 40 pages in about 5 hours. We also know that Jack's rate is slower than Tom's. So if Jack works alone he must take more than double the time it would have taken had they worked together. i.e little more than 10. Only E suffices. P.S. Could anyone let me know if we should follow this approach of using Logic to arrive at the answer if the Work Rate problems become convoluted??(Like involving massive quadratics) Yes, your approach is absolutely fine. If nothing is working out, you can certainly take a very good guess in this way (here the options are such that you would have no doubt that (E) is the correct answer). We just run the risk of more than 1 options satisfying the constraints we come up with at the end. Say, an option gave you 11.6, then we would have wasted time. We cannot use approximation in that case. Therefore, you also need to learn to work on equations where the variable is in the denominator. You don't necessarily have to make a quadratic in that case. You can plug in the options as I have discussed in my post above: ittakesjack2morehoursthantomtotype20pagesif102407.html#p1024552.
_________________
Karishma Veritas Prep GMAT Instructor
Save up to $1,000 on GMAT prep through 8/20! Learn more here >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Manager
Joined: 13 Feb 2011
Posts: 93

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
08 Jul 2014, 09:42
I need some guidance here.. Although I understand the basic work = rate*time formula but when working on problems such as above it doesn't quite strikes me that what is a good way to solve a problem until I end up going through Bunuel or any other expert's post. :l Such as in this problem, rather than assuming variables for time, i assumed variables for rates and came up with: (j+t)*3 = 25 and 20/j = 20/t + 2 where j and t are respective rate variables for Jack and Tom. And while substituting and solving these equations, I got lost and spent 4 minutes without an answer. But as soon as I went through Bunuel's and Karishma's posts I noticed that assuming variables for what was asked (i.e. time) would have made the solution easier.
My question is how/what should one practice in order to get into the habit of approaching the problem in a simpler way rather than just coming up with longroutes and unnecessary calculations that might not be even needed for getting the answer.
I know this question is quite subjective, but any help will be appreciated.
Thanks much!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8196
Location: Pune, India

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
08 Jul 2014, 23:08
Dienekes wrote: I need some guidance here.. Although I understand the basic work = rate*time formula but when working on problems such as above it doesn't quite strikes me that what is a good way to solve a problem until I end up going through Bunuel or any other expert's post. :l Such as in this problem, rather than assuming variables for time, i assumed variables for rates and came up with: (j+t)*3 = 25 and 20/j = 20/t + 2 where j and t are respective rate variables for Jack and Tom. And while substituting and solving these equations, I got lost and spent 4 minutes without an answer. But as soon as I went through Bunuel's and Karishma's posts I noticed that assuming variables for what was asked (i.e. time) would have made the solution easier.
My question is how/what should one practice in order to get into the habit of approaching the problem in a simpler way rather than just coming up with longroutes and unnecessary calculations that might not be even needed for getting the answer.
I know this question is quite subjective, but any help will be appreciated.
Thanks much! Here are a few tips:  Many times, you wont need to take any variables. You can use a logical approach though that takes some work and practice first.  If you do need to take variables, you will usually need to take only one. Let that variable be the one which you need to find. Say, if you need time taken, take the variable T, not rate or work. Very rarely would it be a good idea to take something else as the variable. Also, prefer to work with multiplication and addition rather than division and subtraction i.e. if time take by A is 2 hrs more than time taken by B, assume time taken by B = T and time taken by A = T+2.  Very rarely would you need to take two variables. If you do, find the relation between the two variables as soon as you can and then bring everything down to a single variable. With practice, you will know how to identify the right approach quickly. Sometimes, everyone gets lost in a circuitous method  important is to move on and not waste too much time on it.
_________________
Karishma Veritas Prep GMAT Instructor
Save up to $1,000 on GMAT prep through 8/20! Learn more here >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Manager
Joined: 27 Jan 2013
Posts: 175
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
WE: Supply Chain Management (Telecommunications)

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
24 Feb 2015, 16:00
I did this question in the gmat club test. Couldn't solve it using the traditional approach then used another approach for this. We know that combined they typed 25 pages in 3 hrs. Hence combined they will type 40 pages in 3*40/25=24/5~=5 I considered that since together they take 5 hrs then individually J's time would be more than 10 hours as his speed his lower than that of Tom. The only possible answer is E i.e 12 hrs.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8196
Location: Pune, India

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
25 Feb 2015, 20:14
qw1981 wrote: I did this question in the gmat club test. Couldn't solve it using the traditional approach then used another approach for this. We know that combined they typed 25 pages in 3 hrs. Hence combined they will type 40 pages in 3*40/25=24/5~=5 I considered that since together they take 5 hrs then individually J's time would be more than 10 hours as his speed his lower than that of Tom. The only possible answer is E i.e 12 hrs. Yes, your approach is very good. The only thing I have an issue with is the approximation used. Their combined time is 4.8 hrs and hence we know that Jack will take more than 9.6 hrs. 10 hrs is a possible candidate for the correct option in that case. Though I would say that if Jack took just a wee bit more than 9.6 hrs, then Tom would have taken a tiny bit less than 9.6 hrs and then the difference in their individual time taken could not be 2 hrs. So yes, (E) must be the answer.
_________________
Karishma Veritas Prep GMAT Instructor
Save up to $1,000 on GMAT prep through 8/20! Learn more here >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 12 Mar 2015
Posts: 4

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
05 Oct 2015, 23:05
Barkatis wrote: It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages?
A. 5 B. 6 C. 8 D. 10 E. 12 Hello, why can't it be time taken by tom= T and time taken by Jack= T+2 ? And then the eq becomes \(\frac{20}{T}\) + \(\frac{20}{T+2}\) = \(\frac{25}{3}\) Please help?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8196
Location: Pune, India

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
05 Oct 2015, 23:34
amanlalwani wrote: Barkatis wrote: It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages?
A. 5 B. 6 C. 8 D. 10 E. 12 Hello, why can't it be time taken by tom= T and time taken by Jack= T+2 ? And then the eq becomes \(\frac{20}{T}\) + \(\frac{20}{T+2}\) = \(\frac{25}{3}\) Please help? It can be. If you solve it, you will get T = 4. Then, to get time taken by Jack, you just add 2 to it to get 6 hrs. Note that you can take either variable but it is often better to assume what you have to find (time taken by Jack) since sometimes, we forget the last step. If you directly get the value of J, great. If you first find the value of T, you might forget to add 2 at the end to get the actual answer.
_________________
Karishma Veritas Prep GMAT Instructor
Save up to $1,000 on GMAT prep through 8/20! Learn more here >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 12 Mar 2015
Posts: 4

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
06 Oct 2015, 00:59
VeritasPrepKarishma wrote: amanlalwani wrote: Barkatis wrote: It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages?
A. 5 B. 6 C. 8 D. 10 E. 12 Hello, why can't it be time taken by tom= T and time taken by Jack= T+2 ? And then the eq becomes \(\frac{20}{T}\) + \(\frac{20}{T+2}\) = \(\frac{25}{3}\) Please help? It can be. If you solve it, you will get T = 4. Then, to get time taken by Jack, you just add 2 to it to get 6 hrs. Note that you can take either variable but it is often better to assume what you have to find (time taken by Jack) since sometimes, we forget the last step. If you directly get the value of J, great. If you first find the value of T, you might forget to add 2 at the end to get the actual answer. Thanks Karishma, i understand that taking T2 will ideally be better and it is true that we can forget the thing we need to find at the end.



DS Forum Moderator
Joined: 27 Oct 2017
Posts: 675
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
06 Feb 2018, 07:19
Let Tom takes x hrs and Jack takes x+2 hrs .. so in 1 hr Tom completes 20/x pages and Jack completes 20/(x+2) pages .. Given Both can complete 25 pages in 3 hrs .. so in 1 hr they both can complete 25/3 pages in combination . so 20/x + 20/(x+2) = 25/3 .. on solving we get x = 4 .. so Jack takes 4+2 = 6 hrs to complete 20 pages ..so to complete 40 pages he takes 6*2 = 12 hrs ..
_________________
SC: Confusable words All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory Error log/Key Concepts Combination Concept: Division into groups Question of the Day (QOTD) Free GMAT CATS



Senior Manager
Joined: 31 Jul 2017
Posts: 404
Location: Malaysia
WE: Consulting (Energy and Utilities)

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
06 Feb 2018, 07:40
Barkatis wrote: It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages?
A. 5 B. 6 C. 8 D. 10 E. 12 Let Rate of Tom Work = a, Jack work = b. Given, as per question  \(a*t = b*(t+2) = 20\) 1 \((a+b)*3 = 25\),  2 By Solving Equation 1 & 2 we get, \(t = 4 hours\). Thus Jack takes 6 Hours to type 20 pages & 12 Hours to type 40 pages.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2759

Re: It takes Jack 2 more hours than Tom to type 20 pages. If
[#permalink]
Show Tags
08 Feb 2018, 16:38
Barkatis wrote: It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages?
A. 5 B. 6 C. 8 D. 10 E. 12 We can let Tom’s rate = 20/x and Jack’s rate = 20/(x+2), and their combined rate is 25/3; thus: 20/x + 20/(x+2) = 25/3 Multiplying by 3x(x+2), we have: 20(3)(x + 2) + 20(3x) = 25(x)(x + 2) 60x + 120 + 60x = 25x^2 + 50x 25^x  70x  120 = 0 5x^2  14x  24 = 0 (5x + 6)(x  4) = 0 x = 5/6 or x = 4 Since x can’t be negative, we see that x must be 4, so Jack's rate is 20/6 = 10/3. So it takes him 40/(10/3) = 120/10 = 12 hours to type 40 pages. Alternate Solution: Let’s pick a common multiple of 20, 25 and 40, such as 200, and calculate the number of hours to type that number of pages for each scenario. Since Jack takes 2 more hours than Tom to type 20 pages, it will take Jack 20 more hours than Tom to type 200 pages. Since Jack and Tom working together can type 25 pages in 3 hours, they can type 200 pages in 12 hours. Let’s denote the number of hours for Tom to type 200 pages by t. Then, in one hour, Tom can complete 1/t of the job. Since Jack takes 20 more hours than Tom to do the same job, it will take him t + 20 hours to type 200 pages and he can complete 1/(t + 20) of the job in one hour. Working together, they can complete the same job (200 pages) in 24 hours; thus in one hour, they complete 1/24 of the job. We can create the following equation: 1/t + 1/(t + 20) = 1/24 Let’s mutliply each side by 24t(t + 20): 24(t + 20) + 24t = t(t + 20) 24t + 480 + 24t = t^2 + 20t t^2  28t  480 = 0 (t  40)(t + 12) = 0 t = 40 or t = 12 Since t cannot be negative, t must equal 40. Since it takes Tom 40 hours to type 200 pages, it will take him 1/5 the number of hours to type 1/5 the number of pages (40 pages); thus Tom will type 40 pages in 40 x 1/5 = 12 hours. Answer: E
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: It takes Jack 2 more hours than Tom to type 20 pages. If &nbs
[#permalink]
08 Feb 2018, 16:38



Go to page
1 2
Next
[ 22 posts ]



