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# Rate (m09q05)

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Manager
Status: Preparing myself to break the sound( 700 )-barrier!
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27 Jan 2012, 00:06
IMO, plugging in the answer options is the best way to solve this problem. Seriously!

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28 Jan 2012, 19:13
It takes Jack 2 more hours than Tom to type 20 pages. Working together, Jack and Tom can type
25 pages in 3 hours.

1. Let t be Jack's time in hours for job (20pgs), write rate eq.

r1 + r2 = R

20/t + 20/(t - 2) = [5/4(20)]/3

1a. Factor out 20, and solve quadratic for t > 2.

1/x + 1/(x - 2) = 5/12

t = 6
t - 2 = 4

2. Plug in times for job in eq.1 to determine Jack's rate and Tom rate.

20pgs/6hrs = 3.333
20pgs/4hrs = 5

r1 + r2 = R = 8.333

3. Verify rate together, R, against given information "Jack and Tom can type 25 pages in 3 hours".

If R = 8.333, 25/R should equal 3.

25/8.333 = 3 hours

4. Use Jack's rate to determine how long it will take Jack to type 40 pages

40pages/3.333 = 12 hours

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06 Sep 2012, 23:02
Jack does 1 page in : t+ 2 / 20
T does 1 page in : t / 20
together they do 25 pages in 3 hrs
there fore, 1 page in 3 /25

( t+2 / 20 ) + ( t/20 ) = 3 /25 -- > 1 page

solving t = 1/5 , 20 pages : 4 hr for T and 6 hrs for Jack.

for 40 pages : 8 hrs for T and 12 hrs for Jack..

Please let me know if this is the correct approach...

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Math Expert
Joined: 02 Sep 2009
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07 Sep 2012, 02:16
sapna44 wrote:
Jack does 1 page in : t+ 2 / 20
T does 1 page in : t / 20
together they do 25 pages in 3 hrs
there fore, 1 page in 3 /25

( t+2 / 20 ) + ( t/20 ) = 3 /25 -- > 1 page

solving t = 1/5 , 20 pages : 4 hr for T and 6 hrs for Jack.

for 40 pages : 8 hrs for T and 12 hrs for Jack..

Please let me know if this is the correct approach...

Check this post for correct solutions: rate-m09q05-73633.html#p856920

Hope it helps.
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08 Sep 2012, 05:55
mandb wrote:
Is there an easier way to get the answer?
I can get the formula. But when I find the root it really takes too much time. How do i solve this in 2 min?
Should I back solve by dividing all the answers by 2?

For Time and Work problems, If A takes x hrs to do a work and B takes y hours to do a work they combindly do the work in n hrs

Formula is => 1/x+1/y = 1/n

Here Tom takes x hrs to type 20 pages
So Jack takes (x+2) hrs to type 20 pages

So Tom takes 5x/4 to type 25 Pages => Jack takes 5(x+2)/4 hrs to type 25 pags

They both completed typing in 3 hrs, accoring to above formula (1/(5x/4)) +(1/(5(x+2)/4)) = 1/3

This leads to an equation 5x^2-14x-24 = 0 Since x cannot be less than zero x =4
x = Time taken by Tom to type 20 pages. So Jack takes 6 hrs to type 20 pages => Jack takes 12 hrs to type 40 pages.

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15 Sep 2012, 03:26
If anybody wants it, here's a pure algebra solution (didn't take very long):

J can do 20 pages in J hours; let's call 20 pages "1 job". So J can do 1/j part of job in 1 hour.
T can do 20 pages in T+2 hours; T can do 1/(j - 2) part of job in 1 hour.

Together they can do 1/j + 1/(j - 2) = (2j - 2) / (j^2 - 2j) {common denominator} in 1 hour, so reciprocal:
it takes (j^2 - 2j) / (2j - 2) hours to do 1 job or 20 pages.

It must take 5/4 of this to do 25 pages, which is also stated to be 3 hours. So

5*(j^2 - 2j) / 4*(2j - 2) = 3

which means 5j^2 - 10j = 24j - 24, or 5j^2 - 34j + 24 = 0, or (5j - 4)(j - 6) = 0, {no need for quadratic formula}
so j must be 6 (can't be 5/4 because then no way to subtract 2 hours for Tom).

If j does 20 pages in 6 hours, must do 40 pages in 12 hours.

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GMAT 1: 670 Q49 V33
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24 Dec 2012, 02:10
Bunuel wrote:
This problem was also posted in PS subforum. Below is my solution from there.

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 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.

Hi

Can we solve this question logically, without making equations as mentioned in http://www.veritasprep.com/blog/2011/03 ... -problems/
_________________

YOU CAN, IF YOU THINK YOU CAN

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Math Expert
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24 Dec 2012, 02:13
1
KUDOS
Expert's post
greatps24 wrote:
Bunuel wrote:
This problem was also posted in PS subforum. Below is my solution from there.

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 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.

Hi

Can we solve this question logically, without making equations as mentioned in http://www.veritasprep.com/blog/2011/03 ... -problems/

Check here: it-takes-jack-2-more-hours-than-tom-to-type-20-pages-if-102407.html#p1024552

Hope it helps.
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Senior Manager
Joined: 22 Aug 2013
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05 Sep 2013, 13:30
tinki wrote:
Hellooo ... Can somobody exolain how to solve -5T^2 + 14T + 24 = 0 ? or similar equations? (not the simple ones, they are easily solvable)
with quadratic formula? or any shortcut?
thanks

this equation is same as 5T^2 - 14T - 24 = 0. now we need to find the value(s) of T for which left hand side of this equation will become '0', i.e., value(s) of T for which this equation will be satisfied. One method which sometimes works is the factorisation method which is basically this:

for a quadratic equation ax^2 + bx + c = 0 we first need to find 2 quantities whose sum is 'bx' and product is 'cax^2' and then we can split the middle term accordingly, eg, in your example equation
5T^2 - 14T - 24 = 0 we need to find 2 quantities whose sum is -14T and whose product is 120T^2. the two such quantities are -20T and 6T. so using these the equation can now be written as:

5T^2 - 14T - 24 = 0
5T^2 - 20T + 6T - 24 = 0 ..... now we can factorise easily as:
5T(T - 4) + 6(T - 4) = 0 which gives us
(5T+6)(T-4) = 0 ... now we will put each of the two brackets equal to zero to get two values of T:

5T + 6 = 0 gives us T = -6/5
and T - 4 = 0 gives us T = 4... and these two values are the solution of the equation

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06 Sep 2013, 06:36
Forget all that quadratic equation rubbish, YOU WILL NOT HAVE TO TIME TO DO THIS IN THE EXAM!!!!!

I got the equation, attempted to solve but was already 4mins down or something...

Just sub the answers and get the solution, best way to do it. People don't want to solve it that way on here because it isn't an elegant method, WHO CARES... you get the right answer

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14 Jan 2014, 12:43
Bunuel wrote:
This problem was also posted in PS subforum. Below is my solution from there.

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 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: $$2j=12$$ --> $$j=6$$ --> $$\frac{60}{6}+\frac{60}{6-2}=10+15=25$$.

Hope it helps.

Great explanation, but I used (20/j)+(20/j+2) instead of (20/j)+(20/j-2) and it of course does not work... Why do you subtract 2 from j instead of adding it? Question says "jack takes two hours longer" so it seems natural to add.

Posted from my mobile device

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Math Expert
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15 Jan 2014, 00:38
cf1988 wrote:
Bunuel wrote:
This problem was also posted in PS subforum. Below is my solution from there.

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 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: $$2j=12$$ --> $$j=6$$ --> $$\frac{60}{6}+\frac{60}{6-2}=10+15=25$$.

Hope it helps.

Great explanation, but I used (20/j)+(20/j+2) instead of (20/j)+(20/j-2) and it of course does not work... Why do you subtract 2 from j instead of adding it? Question says "jack takes two hours longer" so it seems natural to add.

Posted from my mobile device

It takes Jack 2 more hours than Tom to do the job --> J is greater than T by 2 --> J = T + 2 --> T = J - 2.

Hope it helps.
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15 Jan 2014, 01:06
It takes Jack 2 more hours than Tom to type 20 pages. Working together, Jack and Tom can type 25 pages in 3 hours. How long will it take Jack to type 40 pages?

(A) 5 hours
(B) 6 hours
(C) 8 hours
(D) 10 hours
(E) 12 hours

Sol: Combined rate of Jack and Tom is 25 pages in 3 hours so 8.33 pages per hour.

Let's take option C So jack takes 8 hours to type 40 pages or 5 pages per hour. For 20 pages Jack will take 4 hours and Tom will take 2 hours to type 20 pages
So, (Jack's rate+Tom's rate)*3= 25 pages but Jack's rate=5 and Tom's rate= 10 so not possible

Option A, B and C can be easily ruled out.

Option D, So Jack's rate: 4 pags per hour So 5 hours to type 20 pages and Tom's rate will 3 hours for 20 pages (Combined rate = 4+6.66)*3 is not equal to 25.

Hence Ans E
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15 Jan 2014, 11:10
It takes Jack 2 more hours than Tom to do the job --> J is greater than T by 2 --> J = T + 2 --> T = J - 2.

Hope it helps.[/quote]

Helped a lot thanks

Posted from my mobile device

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20 Apr 2014, 07:19
Suppose Tom takes a hrs to finish 20 pages -> Jack: a+2 hrs
-> 20/a+20/(a+2)=25/3-> 5a^2-14a-24=0-> a=4-> E:12 hrs

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Re: Rate (m09q05)   [#permalink] 20 Apr 2014, 07:19

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# Rate (m09q05)

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