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# Marla and Evan are reading copies of the same book, at different const

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Math Expert
Joined: 02 Sep 2009
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Marla and Evan are reading copies of the same book, at different const  [#permalink]

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27 Apr 2017, 01:45
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Difficulty:

15% (low)

Question Stats:

78% (01:31) correct 22% (01:27) wrong based on 169 sessions

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Marla and Evan are reading copies of the same book, at different constant rates. Marla reads 80 pages per hour and started reading at 1:00 p.m. while Evan reads 60 pages per hour and started reading at 12:30 p.m. What time will they be reading the same page?

A. 12:30 p.m.
B. 1:30 p.m.
C. 2:00 p.m.
D. 2:30 p.m.
E. 3:00 p.m.

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Re: Marla and Evan are reading copies of the same book, at different const  [#permalink]

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27 Apr 2017, 01:57
Starting at 1PM, Marla will read 20pages an hour extra(Relative speed = Marla's speed - Evan's speed)
Hence, it will take 1.5 hours(Pages to read/Relative speed = 30/20) to read the remaining pages.
Time at which they will be reading the same page is 2:30PM(Option D)
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Marla and Evan are reading copies of the same book, at different const  [#permalink]

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27 Apr 2017, 18:11
------ @1PM ------ @2PM ------------ @3PM
M------ 0 ------------ 80 ------------ 160
E ------ 30 ----------- 90 ------------ 150

The # of pages are increased by a constant rate, here Evan is ahead of Marla at 2PM and Marla bet Evan at 3PM, so answer should be between 2 & 3, Option D

Considering the # of pages covered by Marla and Evan are 40 and 30 for 30 minutes as the rate is constant

Now @ 2:30 Marla will be at 80+40 = 120th page
and Evan wil be at 90 + 30 = 120th page
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Marla and Evan are reading copies of the same book, at different const  [#permalink]

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09 Sep 2018, 07:28
1
Bunuel wrote:
Marla and Evan are reading copies of the same book, at different constant rates. Marla reads 80 pages per hour and started reading at 1:00 p.m. while Evan reads 60 pages per hour and started reading at 12:30 p.m. What time will they be reading the same page?

A. 12:30 p.m.
B. 1:30 p.m.
C. 2:00 p.m.
D. 2:30 p.m.
E. 3:00 p.m.

We can treat this question as a "distance gap" problem in which Marla must "chase" Evan. The distance is number of pages. (Conceptually, number of pages is the same as number of miles)

E's rate: $$\frac{60p}{hr}$$
M's rate: $$\frac{80p}{hr}$$

(1) D gap = # of pages
Before Marla starts, Evan reads a number of pages -- the latter is the distance gap.

From 12:30 to 1:00, Evan read $$\frac{1}{2}$$ hour, alone. r*t= D
E read $$(\frac{60p}{hr}*\frac{1}{2}hr)=30$$ pages
$$D_{gap}=30$$ pages

(2) Rate at which the gap closes?
M must catch E in a "chase." They read in the same direction. Subtract slower from faster rate for relative speed:
$$(R_{M}-R_{E})=(80-60)=20$$ pgs per hr

Time needed to close the gap?
$$D_{gap}=30$$ pages
$$r_{rel}=20$$ pages per hour
$$r*t=D$$, so $$t=\frac{D}{r}$$
Time, T, needed to cover the "distance" and close the gap: $$\frac{30}{20}=\frac{3}{2}=1.5$$ hrs

(3) Ending time?
We use Marla's start time to calculate finish time. She chases and catches Evan at the relative rate when BOTH are reading.
Marla started at 1:00 p.m.
1.5 hours later is 2:30 p.m.

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Joined: 29 May 2017
Posts: 127
Location: Pakistan
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Re: Marla and Evan are reading copies of the same book, at different const  [#permalink]

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25 Sep 2018, 17:13
can this question be done using the LCM/GCF?
Intern
Joined: 29 Dec 2014
Posts: 18
Re: Marla and Evan are reading copies of the same book, at different const  [#permalink]

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25 Sep 2018, 17:29
D ivan is 30 pages ahead so in one hour Marla covered 20 pages i.e 80-60 so 1 hour 30 from 1 i.e 2.30

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Re: Marla and Evan are reading copies of the same book, at different const  [#permalink]

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01 Oct 2018, 05:32
Marla will read 20 pages an hour extra (Relative speed = Marla's speed - Evan's speed)
$$R_s=M_s-E_s$$ => 80-60=20 pages/hour

T=W/R
so, T=30/20=>1.5 hrs
As, Marla has to catch up Evan so starting 1 pm, they will be on the same page at 2:30 pm.

(D)
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Joined: 25 Aug 2018
Posts: 1
Re: Marla and Evan are reading copies of the same book, at different const  [#permalink]

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17 Nov 2018, 14:19
generis wrote:
Bunuel wrote:
Marla and Evan are reading copies of the same book, at different constant rates. Marla reads 80 pages per hour and started reading at 1:00 p.m. while Evan reads 60 pages per hour and started reading at 12:30 p.m. What time will they be reading the same page?

A. 12:30 p.m.
B. 1:30 p.m.
C. 2:00 p.m.
D. 2:30 p.m.
E. 3:00 p.m.

We can treat this question as a "distance gap" problem in which Marla must "chase" Evan. The distance is number of pages. (Conceptually, number of pages is the same as number of miles)

E's rate: $$\frac{60p}{hr}$$
M's rate: $$\frac{80p}{hr}$$

(1) D gap = # of pages
Before Marla starts, Evan reads a number of pages -- the latter is the distance gap.

From 12:30 to 1:00, Evan read $$\frac{1}{2}$$ hour, alone. r*t= D
E read $$(\frac{60p}{hr}*\frac{1}{2}hr)=30$$ pages
$$D_{gap}=30$$ pages

(2) Rate at which the gap closes?
M must catch E in a "chase." They read in the same direction. Subtract slower from faster rate for relative speed:
$$(R_{M}-R_{E})=(80-60)=20$$ pgs per hr

Time needed to close the gap?
$$D_{gap}=30$$ pages
$$r_{rel}=20$$ pages per hour
$$r*t=D$$, so $$t=\frac{D}{r}$$
Time, T, needed to cover the "distance" and close the gap: $$\frac{30}{20}=\frac{3}{2}=1.5$$ hrs

(3) Ending time?
We use Marla's start time to calculate finish time. She chases and catches Evan at the relative rate when BOTH are reading.
Marla started at 1:00 p.m.
1.5 hours later is 2:30 p.m.

This was super well explained, thank you!!
Re: Marla and Evan are reading copies of the same book, at different const &nbs [#permalink] 17 Nov 2018, 14:19
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