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Working together, John and Jack can type 20 pages in one hou

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Working together, John and Jack can type 20 pages in one hou [#permalink] New post 09 Oct 2010, 00:26
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Working together, John and Jack can type 20 pages in one hour. If they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?

A. 1/3
B. 2/5
C. 1/2
D. 2/3
E. 3/5
[Reveal] Spoiler: OA
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Re: Hours to type pages [#permalink] New post 09 Oct 2010, 00:44
Here is the way I solve it using the formula RATE = JOB / TIME

Let x be the Job done by Jack in one hour and y the job done by Johon in one hour.

Working together, John and Jack can type 20 pages in one hour : x/1 + y/1 = 20/1

they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%: 5/4(x/1) + y/1 = 22/1

Thus x=8 ; y=12
x/y = 2/3
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Re: Hours to type pages [#permalink] New post 09 Oct 2010, 00:50
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Barkatis wrote:
how would you solve this one ?

Working together, John and Jack can type 20 pages in one hour. If they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?

1/3
2/5
1/2
2/3
3/5


Lets say John types x pages an hour and Jack types y pages an hour.

We know that x+y=20

Jack increase speed by 25% means he will type 1.25y pages an hour.

So we get x+1.25y=22

We need to know the ratio of Jack's speed to John's speed. This is going to be proportional to the number of pages each can type in an hour, hence (y/x).

Subtracting both : 0.25y=2 so y=8 ... so x=12
(y/x)=2/3

Answer is (D)
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Re: Hours to type pages [#permalink] New post 09 Oct 2010, 00:51
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Barkatis wrote:
how would you solve this one ?

Working together, John and Jack can type 20 pages in one hour. If they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?

1/3
2/5
1/2
2/3
3/5


Let the rate of John be x pages per hour and the rate of Jack y pages per hour. Then as we can sum the rates and rate*time=job: (x+y)*1=20 --> x+y=20;

"They would be able to type 22 pages in one hour if Jack increases his typing speed by 25%": (x+1.25y)*1=22 --> x+1.25y=22;

Question: \frac{y}{x}=?

Subtract (1) from (2) --> x+1.25y-(x+y)=22-20 --> 0.25y=2 --> y=8 --> x=12 --> \frac{y}{x}=\frac{8}{12}=\frac{2}{3}.

Answer: D.

OR: as by increasing the rate of Jack by 25% 2 more pages can be typed in one hour than we can directly write: 0.25y=2 --> --> y=8 --> x=12 --> \frac{y}{x}=\frac{8}{12}=\frac{2}{3}.

Answer: D.
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Re: Hours to type pages [#permalink] New post 30 Nov 2011, 22:07
Let the rate of John be x pages per hour and the rate of Jack y pages per hour.

so x + y = 20------------(i)
After 25% increase by y
x + 1.25y = 22-----------(ii)
Solving i and ii
y = 8
x = 12
Ratio = 2/3
Ans. D
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Re: Hours to type pages [#permalink] New post 01 Dec 2011, 04:14
x+y=20
4x+5y=88
x=8
y=12

==>D
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Re: Hours to type pages [#permalink] New post 22 Dec 2011, 01:22
D is the answer. Quite an easy one.
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Re: Working together, John and Jack can type 20 pages in one hou [#permalink] New post 07 Nov 2013, 09:17
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Re: Working together, John and Jack can type 20 pages in one hou   [#permalink] 07 Nov 2013, 09:17
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