GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 17 Feb 2020, 00:57

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Intern
Status: never give up on yourself
Joined: 14 Apr 2018
Posts: 6
WE: Corporate Finance (Accounting)
Re: It takes Jack 2 more hours than Tom to type 20 pages. If  [#permalink]

### Show Tags

20 Jun 2018, 03:53
VeritasPrepKarishma 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?

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.

can you please explain what is wrong with my method
rate of jack =1/x
rate of tom=1/x-2
working together they will take=1/x + 1/x-2 = 1/3
i am not getting the correct answer
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10098
Location: Pune, India
Re: It takes Jack 2 more hours than Tom to type 20 pages. If  [#permalink]

### Show Tags

20 Jun 2018, 04:35
Abhishekgmatfit wrote:
VeritasPrepKarishma 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?

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.

can you please explain what is wrong with my method
rate of jack =1/x
rate of tom=1/x-2
working together they will take=1/x + 1/x-2 = 1/3
i am not getting the correct answer

How does 1/x + 1/x-2 equal 1/3?

$$\frac{1}{x} + \frac{1}{(x-2)} = \frac{(2x - 2)}{x(x - 2)} = \frac{5}{12}$$

Note how you get 5/12 - The combined rate is 25 pages in 3 hrs. But initially our work done was 20 pages which would then be done in (4/5)*3 = 12/5 hrs. So combined rate is 5/12.

When you solve the above, you get x = 6.

So Jack types 20 pages in 6 hrs. He will type 40 pages in 12 hrs.
_________________
Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 10 Jul 2016
Posts: 44
Re: It takes Jack 2 more hours than Tom to type 20 pages. If  [#permalink]

### Show Tags

26 Feb 2019, 18:37
JeffTargetTestPrep 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

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.

Hi Jeff,

SVP
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1698
Location: India
GPA: 3.01
WE: Engineering (Real Estate)
Re: It takes Jack 2 more hours than Tom to type 20 pages. If  [#permalink]

### Show Tags

27 Feb 2019, 03:47
1
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 us say Tom's time = t hours

So, Jack's time = t + 2 hours ----- (I)

Work (1) = 20 pages

Therefore Tom's rate = $$\frac{20}{t}$$

Jack's rate = $$\frac{20}{(t+2)}$$ -------- (II)

Now, Work (2) = 25 pages

Time = 3 hours

Work done by Tom + Work done by Jack = Total Work

$$\frac{20}{t}$$ * 3 + $$\frac{20}{(t+2)}$$ * 3 = 25

Solving this becomes ,

$$25t^2 - 70t - 120t = 0$$

Divide by 5 ; $$5t^2 - 14t - 24 = 0$$

$$5t^2 - 20t + 6t - 24 = 0$$

$$5t (t - 4) + 6 (t - 4) = 0$$

t = 4 or t = -6/5 , Reject negative solution

Jack's rate =$$\frac{20}{(t + 2)}$$ = $$\frac{20}{6}$$ as per equation (II) above

New Work (3) = 40 pages

Time required for Jack to complete the work = $$\frac{(40*6)}{20}$$

_________________
"Do not watch clock; Do what it does. KEEP GOING."
Re: It takes Jack 2 more hours than Tom to type 20 pages. If   [#permalink] 27 Feb 2019, 03:47

Go to page   Previous    1   2   [ 24 posts ]

Display posts from previous: Sort by