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Linda and Bobby are reading copies of the same book, at different cons

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Linda and Bobby are reading copies of the same book, at different cons  [#permalink]

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New post 22 Jan 2018, 23:22
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

54% (03:06) correct 46% (03:08) wrong based on 70 sessions

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Linda and Bobby are reading copies of the same book, at different constant rates. Linda reads 75 pages per hour and started reading at 1:15 p.m. while Bobby reads 52 pages per hour and started reading at 12:30 p.m. What time will they be reading the same page?

A. 2:10 p.m.
B. 2:27 p.m.
C. 2:34 p.m.
D. 2:56 p.m.
E. 3:00 p.m.

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Re: Linda and Bobby are reading copies of the same book, at different cons  [#permalink]

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New post 23 Jan 2018, 02:12
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Bunuel wrote:
Linda and Bobby are reading copies of the same book, at different constant rates. Linda reads 75 pages per hour and started reading at 1:15 p.m. while Bobby reads 52 pages per hour and started reading at 12:30 p.m. What time will they be reading the same page?

A. 2:10 p.m.
B. 2:27 p.m.
C. 2:34 p.m.
D. 2:56 p.m.
E. 3:00 p.m.



Linda reads 75 pages per hour

Bobby reads 52 pages per hour

i.e, Relative speed @which the gap between the read pages change = 75-52 = 23 pages per hour

Headstart of Bobby = Pages read in 15+30 i.e 45 minutes i.e. 3/4 hours (From 1:15 to 12:30) = 52*3/4 = 13*3 pages

The time to finish the gap between the two = Total Gap / Rate at which the gap changes = 39/23 = 1.7 hours = 1 hours 42 minutes

Answer: Option D
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Re: Linda and Bobby are reading copies of the same book, at different cons  [#permalink]

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New post 24 Jan 2018, 10:33
1
Bunuel wrote:
Linda and Bobby are reading copies of the same book, at different constant rates. Linda reads 75 pages per hour and started reading at 1:15 p.m. while Bobby reads 52 pages per hour and started reading at 12:30 p.m. What time will they be reading the same page?

A. 2:10 p.m.
B. 2:27 p.m.
C. 2:34 p.m.
D. 2:56 p.m.
E. 3:00 p.m.


Lindas rate is 75 pages per hour and Bobby’s is 52 pages per hour. Converting 45 minutes to 3/4 hour, we can let Bobby’s time = t + 3/4 and Linda’s time = t. Let’s determine the time it will take for them to be on the same page:

52(t + 3/4) = 75t

52t + 39 = 75t

39 = 23t

39/23 = t

The answer of 39/23 hours = 39/23 x 60 ≈ 101.7 minutes. Thus, they will be on the same page 101 minutes after Linda began at 1:15 p.m. Since 101 minutes = 1 hr 41 min, thus they will be on the same page at:

1:15 p.m. + 1 hr 41 min = 2:56 p.m.

Answer: D
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Re: Linda and Bobby are reading copies of the same book, at different cons   [#permalink] 24 Jan 2018, 10:33
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