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Adam and John simultaneously begin to write out a booklet containing

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DisciplinedPrep
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Adam and John simultaneously begin to write out a booklet containing [#permalink] New post  02 May 2019, 17:12
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65% (02:33) correct 35% (02:45) wrong based on 176 sessions
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Adam and John simultaneously begin to write out a booklet containing 535 lines. Adam starts with the first line, writing at the rate of 100 lines an hour, and John starts with the last line and moves backward, proceeding at the rate of 50 lines an hour. At what line will they meet?

A. 356
B. 277
C. 357
D. 267
E. 435
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GyanOne
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Adam and John simultaneously begin to write out a booklet containing [#permalink] New post  02 May 2019, 20:30
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Quickest way to solve this question with minimal calculations:

Adam writes at twice the rate of John. Therefore in the time that John covers x, Adam will cover 2x.
=> They will meet at (2/3) of the length of the book.
=> They will meet at page 535*2/3 = page 357

Option (C).

PS - For anyone confused between Option (A) and (C), note that 535*(2/3) = 356.66, which is more than 356, or the 357th page.
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stne
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Adam and John simultaneously begin to write out a booklet containing [#permalink] New post  06 May 2019, 05:08
GyanOne wrote:
Quickest way to solve this question with minimal calculations:

Adam writes at twice the rate of John. Therefore in the time that John covers x, Adam will cover 2x.
=> They will meet at (2/3) of the length of the book.
=> They will meet at page 535*2/3 = page 357

Option (C).

PS - For anyone confused between Option (A) and (C), note that 535*(2/3) = 356.66, which is more than 356, or the 357th page.



Awesome solution! by GyanOne

another soln: Let them meet at time T then 100T+50T=535
T=107/30 , so in this much time adam would be at line, 100 *\(\frac{107}{30}\)=356.66 or 357 line .
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Adam and John simultaneously begin to write out a booklet containing [#permalink] New post  25 May 2019, 07:33
This problem can be seen as a rate/speed problem where two objects will collide each other.

Speed of Adam = 100 lines/hr; Speed of John = 50 lines/hr
Relative speed = 150 lines/hr

Distance = 535 lines

S= D/T
T= 107/30 hr is the time at which Adam and John will meet.

Distance covered by Adam = S*T = 100*(107/30) = 356.67 ~ 357 lines

Ans - C

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Sreeragc
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Re: Adam and John simultaneously begin to write out a booklet containing [#permalink] New post  12 Jun 2019, 11:00
GyanOne wrote:
Quickest way to solve this question with minimal calculations:

Adam writes at twice the rate of John. Therefore in the time that John covers x, Adam will cover 2x.
=> They will meet at (2/3) of the length of the book.
=> They will meet at page 535*2/3 = page 357

Option (C).

PS - For anyone confused between Option (A) and (C), note that 535*(2/3) = 356.66, which is more than 356, or the 357th page.




How did we know that they meet at 2/3 of the length of the book??
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aliakberza
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Re: Adam and John simultaneously begin to write out a booklet containing [#permalink] New post  14 Jun 2019, 17:00
Sreeragc wrote:
GyanOne wrote:
Quickest way to solve this question with minimal calculations:

Adam writes at twice the rate of John. Therefore in the time that John covers x, Adam will cover 2x.
=> They will meet at (2/3) of the length of the book.
=> They will meet at page 535*2/3 = page 357

Option (C).

PS - For anyone confused between Option (A) and (C), note that 535*(2/3) = 356.66, which is more than 356, or the 357th page.




How did we know that they meet at 2/3 of the length of the book??


Sreeragc


Because Adam's speed is twice John's speed, so:
after 1 hour : Adam writes 100 lines and John writes 50 lines; total lines 150 of which Adam wrote 2/3rds and John wrote 1/3rds
after 2 hours: Adam would have written 200 lines and John 100 lines; total lines 300 of which Adam wrote 2/3rds and John wrote 1/3rds

The ratio will always be 1:2 and Adam would have always written 2/3rds of the total lines written. Since John is working from the bottom and Adam from the top, they will meet when they have collectively written all of the 535 lines. Counting from the beginning that would be 2/3 * 535 ~= 357 lines. Hope this clears it up.
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KarishmaB
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Re: Adam and John simultaneously begin to write out a booklet containing [#permalink] New post  16 Sep 2023, 09:52
Expert Reply
DisciplinedPrep wrote:
Adam and John simultaneously begin to write out a booklet containing 535 lines. Adam starts with the first line, writing at the rate of 100 lines an hour, and John starts with the last line and moves backward, proceeding at the rate of 50 lines an hour. At what line will they meet?

A. 356
B. 277
C. 357
D. 267
E. 435


You can also think of this as a relative speed question. At their respective speeds of 100 lines/hr and 50 lines/hr, they have to together cover 535 lines of distance.

\(Time Taken = \frac{535}{(100 + 50)} = \frac{535}{150}\)

In this time, Adam would have written \(\frac{535}{150}*100\) lines = 356.6 lines i.e. He will be on the 357th line (even if this were 356.1, he would still be on the 357th line)

Answer (C)

For basics of work rate, check this video: https://youtu.be/88NFTttkJmA
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Re: Adam and John simultaneously begin to write out a booklet containing [#permalink]
16 Sep 2023, 09:52
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