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Tom reads at an average rate of 30 pages per hour.....

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Joined: 05 Jan 2006
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Tom reads at an average rate of 30 pages per hour.....  [#permalink]

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New post 22 Jan 2006, 14:15
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Could anyone please suggest what is the best way to solve a question like this...

1. Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 40 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:20, at what time will they be reading the same page?

A) 9:30
B) 9:00
C) 8:40
D) 7:50
E) 7:00

2. Steve get on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce get on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?

A) 19
B) 28
C) 30
D) 32
E) 44

3. George takes 8 hours to copy a 50 page manuscript while Sonya can copy the same manuscript in 6 hours. How many hours would it take them to copy a 100 page manuscropt, if they work together?

A) 6 6/7
B) 9
C) 9 5/7
D) 10 2/3
E) 14

Thanks,
Heather

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Re: Tom reads at an average rate of 30 pages per hour.....  [#permalink]

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New post 22 Jan 2006, 21:46
1
The key to solve these problems is to be diligent and write the steps carefully..once you get comfortable you will notice short cuts that you can employ. 1 and 2 have been posted in the forum before.

I will solve 3 :
Rate of George 50/8 pages/hour.
Rate of Sonja 50/6 pages/hour.

Combined rate = 50/8 + 50/6 = 700/48.

To copy 700/48 pages it takes them 1 hour, to copy 100 pages it will taken them (100*1)/(700/48) = 48/7 = 6 6/7.

A will the answer.



hedder02 wrote:
Could anyone please suggest what is the best way to solve a question like this...

1. Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 40 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:20, at what time will they be reading the same page?

A) 9:30
B) 9:00
C) 8:40
D) 7:50
E) 7:00

2. Steve get on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce get on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?

A) 19
B) 28
C) 30
D) 32
E) 44

3. George takes 8 hours to copy a 50 page manuscript while Sonya can copy the same manuscript in 6 hours. How many hours would it take them to copy a 100 page manuscropt, if they work together?

A) 6 6/7
B) 9
C) 9 5/7
D) 10 2/3
E) 14

Thanks,
Heather
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New post Updated on: 24 Jan 2006, 00:08
4
1
To solve these questions 1. Assume something as x, which is asked. 2.Write the information one by one from the question.

By doing more and more practice you will be comfortable with these questions.

Q1:

Lets say they met at page x.

So time taken by Tom to read x pages = x/30 hours
So time taken by Jan to read x pages = x/40 hours

But the difference between their start is 5/6 hours

So x/30 - x/40 = 5/6. Solving this we get x = 100

Jan will read 100 pages in 2:30 hours. So 5:20 + 2:30 = 7:50

Q2:

Let they met at floor x.

Time taken by Steve to get to x = (x-11)/57
Time taken by Joyce to get to x = (51-x)/63

These times are equal. Solve the equation and you will get x = 30

Q3:

George's rate = 50/8 pages per hour

Sonya's rate = 50/6 pages per hour

Combined rate = 50/8 + 50/6 = 175/12 pages per hour

Time they will take for to copy 100 pages = Total pages/rate = 100/(175/12) = 100*12/175 = 48/7 = 6 6/7
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Originally posted by ps_dahiya on 23 Jan 2006, 02:03.
Last edited by ps_dahiya on 24 Jan 2006, 00:08, edited 1 time in total.
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New post 23 Jan 2006, 23:31
good one nailed 1 and 3 , thnks dahiya for the solution
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Tom reads at an average rate of 30 pages per hour.....  [#permalink]

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New post 09 Jul 2015, 22:20
1
Quote:
Could anyone please suggest what is the best way to solve a question like this...

1. Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 40 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:20, at what time will they be reading the same page?

A) 9:30
B) 9:00
C) 8:40
D) 7:50
E) 7:00


SOLUTION: Tom starts (@4:40) reading 50 mins before Jan starts (@5:20)
in 60 mins Tome reads 30 pages
i.e. in 50 mins Tome reads 25 pages

Relative Speed = 40-30 = 10 pages per Hour (i.e. the gap of 10 pages will reduce per Hour after Jan starts reading)
Time taken to overcome Gap of 25 pages = (1/10)*25 = 2.5 hours (after 5:20) i.e. 7:50
Answer: Option D


Quote:
2. Steve get on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce get on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?

A) 19
B) 28
C) 30
D) 32
E) 44


SOLUTION: Distance between Steve and Joyce = 51-11 = 40 floors
Relative Speed = 57+63 = 120 Floors per min
Time taken by them to cover the Distance of 40 floors = 40/120 = 1/3 min
Floors crossed by Steve in 1/3 min = 57/3 = 19
i.e. Steve will be at floor no 11+19 = 30 while crossing Joyce
Answer: Option C

Quote:
3. George takes 8 hours to copy a 50 page manuscript while Sonya can copy the same manuscript in 6 hours. How many hours would it take them to copy a 100 page manuscropt, if they work together?

A) 6 6/7
B) 9
C) 9 5/7
D) 10 2/3
E) 14

SOLUTION:George copies 50 pages in 8 hours
i.e. 50/8 pages per hour
Sonya copies 50 pages in 6 hours
i.e. 50/6 pages per hour

Both copy (50/8)+(50/6) pages in 1 hours = 350/24 pages
100 pages will be copied in time = (24/350)*100 = 6 6/7 hours
Answer: Option A
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Re: Tom reads at an average rate of 30 pages per hour.....  [#permalink]

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New post 16 Jul 2018, 17:53
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Re: Tom reads at an average rate of 30 pages per hour..... &nbs [#permalink] 16 Jul 2018, 17:53
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