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# It takes Jack 2 more hours than Tom to type 20 pages. If

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It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink]  07 Oct 2010, 09:49
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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
[Reveal] Spoiler: OA
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Re: Hours to type pages [#permalink]  07 Oct 2010, 10:09
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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 $$j-2$$ hours. So the rate of Jack is $$rate=\frac{job}{time}=\frac{20}{j}$$ pages per hour and the rate of Tom $$rate=\frac{job}{time}=\frac{20}{j-2}$$ pages per hour.

Their combined rate would be $$\frac{20}{j}+\frac{20}{j-2}$$ pages per hour and this equal to $$\frac{25}{3}$$ pages per hour --> $$\frac{20}{j}+\frac{20}{j-2}=\frac{25}{3}$$ --> $$\frac{60}{j}+\frac{60}{j-2}=25$$. 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: $$2j=12$$ --> $$j=6$$ --> $$\frac{60}{6}+\frac{60}{6-2}=10+15=25$$.

Some work problems with solutions:
time-n-work-problem-82718.html?hilit=reciprocal%20rate
facing-problem-with-this-question-91187.html?highlight=rate+reciprocal
what-am-i-doing-wrong-to-bunuel-91124.html?highlight=rate+reciprocal
gmat-prep-ps-93365.html?hilit=reciprocal%20rate
a-good-one-98479.html?hilit=rate
solution-required-100221.html?hilit=work%20rate%20done
work-problem-98599.html?hilit=work%20rate%20done

Hope it helps.
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Re: Hours to type pages [#permalink]  26 Jan 2011, 12:24
Bunuel, I noticed that many sample questions work-rate-questions-i-collected-from-gmat-club-73382.html
result in quadratic equations at some stages. As a rule of thumb, once we faced with a quadratic expression, shall we try answer choices? Maybe I am too slow, but it takes more than 2 min to solve a quadratic expression IN THESE PARTICULAR RATE PROBLEMS.

Thanks for guidance
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Re: Hours to type pages [#permalink]  06 Jan 2012, 01:17
Took ages to complete because of the quadratic equation. Back solving using the options given, IMO, should be a lot faster. Thanks Bunuel.
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Re: Hours to type pages [#permalink]  06 Jan 2012, 02:29
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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.
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Re: It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink]  04 Nov 2012, 07:06
we can back solve it too

lets take answer choice D -10 h

if it took 10 h for 40 pages, then it took 5 hours for 20 pages

since it takes Jack 2 more hours than Tom to type 20 pages, Tom's time is 5-2=3 h

their combo time 5*3 /(5+3)=15/8

if it takes 3 h for 25 pages, then it will take 12/5 h ( =20*3/25) for 20 pages

as u see 15/8 <12/5 . so D is out, and we should check E, whose number is more than D's

answer choice E = 12 for 40 pages or 6 for 20 pages
then Tom's time =6-2=4 h
combo time =6*4/(6+4)=12/5 Bingo!

if it takes 3 h for 25 pages, then it will take 12/5 h ( =20*3/25) for 20 pages

12/5=12/5

answer choice E is the right one
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Re: Hours to type pages [#permalink]  10 Nov 2012, 14:03
Bunuel wrote:
Let the time needed for Jack to type 20 pages by $$j$$ hours, then for Tom it would be $$j-2$$ hours. So the rate of Jack is $$rate=\frac{job}{time}=\frac{20}{j}$$ pages per hour and the rate of Tom $$rate=\frac{job}{time}=\frac{20}{j-2}$$ pages per hour.

Their combined rate would be $$\frac{20}{j}+\frac{20}{j-2}$$ pages per hour and this equal to $$\frac{25}{3}$$ pages per hour --> $$\frac{20}{j}+\frac{20}{j-2}=\frac{25}{3}$$ --> $$\frac{60}{j}+\frac{60}{j-2}=25$$. 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: $$2j=12$$ --> $$j=6$$ --> $$\frac{60}{6}+\frac{60}{6-2}=10+15=25$$.

Bunuel, can you explain how below is possible? Combined 20 pg and equaled to 25 pg?

Their combined rate would be $$\frac{20}{j}+\frac{20}{j-2}$$ pages per hour and this equal to $$\frac{25}{3}$$ pages per hour --> $$\frac{20}{j}+\frac{20}{j-2}=\frac{25}{3}$$
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Re: Hours to type pages [#permalink]  12 Nov 2012, 08:41
Expert's post
gmatchase wrote:
Bunuel wrote:
Let the time needed for Jack to type 20 pages by $$j$$ hours, then for Tom it would be $$j-2$$ hours. So the rate of Jack is $$rate=\frac{job}{time}=\frac{20}{j}$$ pages per hour and the rate of Tom $$rate=\frac{job}{time}=\frac{20}{j-2}$$ pages per hour.

Their combined rate would be $$\frac{20}{j}+\frac{20}{j-2}$$ pages per hour and this equal to $$\frac{25}{3}$$ pages per hour --> $$\frac{20}{j}+\frac{20}{j-2}=\frac{25}{3}$$ --> $$\frac{60}{j}+\frac{60}{j-2}=25$$. 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: $$2j=12$$ --> $$j=6$$ --> $$\frac{60}{6}+\frac{60}{6-2}=10+15=25$$.

Bunuel, can you explain how below is possible? Combined 20 pg and equaled to 25 pg?

Their combined rate would be $$\frac{20}{j}+\frac{20}{j-2}$$ pages per hour and this equal to $$\frac{25}{3}$$ pages per hour --> $$\frac{20}{j}+\frac{20}{j-2}=\frac{25}{3}$$

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/(j-2) pages per hour, thus their combined rate is 20/j+20/(j-2) pages per hour.

So, we have that 20/j+20/(j-2)=25/3.

Hope it's clear.
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Re: It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink]  13 Nov 2012, 21:44
Time it takes Jack and Tom to print 20 pages:
j = t + 2, t = j - 2

Rate Equation:
20/j + 20/j-2 = 25/3
1/j + 1/j-2 = 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!

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Re: It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink]  12 Feb 2013, 11:44
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??????????
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Re: It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink]  12 Feb 2013, 19:10
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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.
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Re: It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink]  03 Mar 2013, 01:27
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)
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Re: It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink]  03 Mar 2013, 21:52
Expert's post
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: it-takes-jack-2-more-hours-than-tom-to-type-20-pages-if-102407.html#p1024552.
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Re: Work problem!!! [#permalink]  28 Sep 2013, 09:09
Rate (J) = 20/t
Rate (T) = 20/(t-2)

20/t + 20/(t-2) = 25/3 (Combined Rate)

t=6 or t=4/5

t=4/5 cannot be the case since t-2 would be negative then!

t=6 for 20 pages
for 40 pages it would be 2t

12
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Re: It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink]  08 Jul 2014, 08:42
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 long-routes 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!
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Re: It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink]  08 Jul 2014, 22:08
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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 long-routes 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.
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Re: It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink]  24 Feb 2015, 15:00
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.
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Re: It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink]  25 Feb 2015, 19:14
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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.
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Re: It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink]  26 Feb 2015, 01:04
VeritasPrepKarishma wrote:
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.

Well i was doing this under time pressure so in the mock exam. So didn't think much about. After wasting some time was about to give up, had an epiphany the approach worked, I marked the answer and moved on
Re: It takes Jack 2 more hours than Tom to type 20 pages. If   [#permalink] 26 Feb 2015, 01:04
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