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It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink]
07 Oct 2010, 09:49

2

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A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

62% (03:32) correct
37% (02:23) wrong based on 203 sessions

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?

Re: Hours to type pages [#permalink]
07 Oct 2010, 10:09

7

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Expert's post

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.

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.

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. Answer: E _________________

Re: Hours to type pages [#permalink]
06 Jan 2012, 02:29

2

This post received KUDOS

Expert's post

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: 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}

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.

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??????????

Re: It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink]
12 Feb 2013, 19:10

Expert's post

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.
_________________

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)

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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