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Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of

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Math Expert

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Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of [#permalink]

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13 Dec 2015, 04:02

00:00

Difficulty:

65% (hard)

Question Stats:

63% (02:19) correct

37% (02:33) wrong

based on 284 sessions

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Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of 30 pages per hour. Michelle begins reading a copy of the same book at 6: 00 p.m. If Michelle started 5 pages behind the page that Ron started on and reads at an average pace of 50 pages per hour, at what time would Ron and Michelle be reading the same page?

A. 7: 00 p.m.
B. 7: 30 p.m.
C. 7: 45 p.m.
D. 8: 00 p.m.
E. 8: 30 p.m.

Spoiler: OA

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Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of [#permalink]

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13 Dec 2015, 09:09

M gains 50-30=20 pages per hour on R
at 6pm R has read 45 pages and M is 45+5=50 pages behind him
time=50/20=2.5 hours
they are on the same page at 8:30pm

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Re: Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of [#permalink]

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13 Dec 2015, 09:39

Ron's speed is 30 pages per hour =1/2 page per minute
Time at which he starts reading is 4:30 pm
now,
by the time Michelle beings reading (6:00 pm) Ron has already covered (1/2)*90=45 pages
as per the question
Michelle starts 5 pages behind the page Ron started and her speed is 5/6 pages per minute
relative speed = 5/6-1/2=1/3
pages left =45+5=50
time taken to read those pages =50/(1/3)=150 minutes
Thus time taken to reach the same page
6:00 pm + (150 minutes) =8:30 pm

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Re: Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of [#permalink]

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14 Dec 2015, 13:01

here's how i took it.... Ron started walking at 4.30 PM, with a constant speed of 30mph. Michelle started travelling in the same direction at 6.00PM, with a speed of 50mph, but started 5 kms behind the point from where Ron started.
in 1.5 hours ron travelled 45 kms, so the distance bw ron and michelle at 6.00 pm (when michelle started) was 45+5=50 miles.
so, the cumulative speed is 50-30=20 mph, distance is 50, time taken is 2.5 hrs.(50/20)
Hence they will be at the same point at 8.30 pm.....
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Re: Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of [#permalink]

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15 Dec 2015, 14:38

IMO answer is 'D'

Till 8 O'clock ron will read- 30X3 +15= 105 pages
Till 8 O'Clock Michelle will read= 2X50 +5= 105 pages

I back calculated for this question.
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Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of [#permalink]

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17 Dec 2015, 01:33

IMO the correct is D.

The number of pages Ron ahead Michelle when he starts to read: 30 *1.5 = 45 pages.
Since Michelle starts 5 pages behind the page that Ron started: the distance between R & M = 45-5 =40 pages.
Time taken by Michelle to catch up with Ron: 40/ (50-30) = 2 hours.
Therefore, the time when both meet is: 6 + 2 = 8pm.
Correct me if I am wrong.
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Re: Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of [#permalink]

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17 Dec 2015, 04:36

HEARTOFWOLF wrote:

The above should be 45 + 5 and not 45 -5 as she has to read additional 5 pages !!

Now,
let us take 8 pm to be the answer !!

for Ron
0.5 pages per minute
time elapsed till 8 pm =210 minutes
pages read by Ron =105 pages

for Michelle time elapsed till 8 pm =120 minutes
thus pages read= 120*5/6=100 pages (minus 5 pages as she started 5 pages behind Ron)

she is actually on 100 -5 = 95

Does not match !!

now add 30 more minutes !!

pages read by Ron =120

pages read by Michelle =150*5/6 = 125 (again minus 5 pages ) =120

MATCH !!

Thus it should be 8:30 pm

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Re: Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of [#permalink]

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11 Jan 2016, 20:46

Bunuel wrote:

Used the answer choices. I still got it wrong due to a really silly mistake. :lol:

A. Ron - 2.5 hours - 75 pages; Michelle - 1 hour - 50 - 5 = 45
B. Ron - 3 hours - 90 pages; Michelle - 1.5 hours - 75 - 5 = 70 pages
C. Ron - 3.25 hours - 97.5 pages; Michelle - 1.75 hours - 87.5 - 5 = 82.5 pages
D. Ron - 3.5 hours - 105 pages; Michelle - 2 hours - 100 - 5 = 95 pages
E. Ron - 4 hours - 120 pages; Michelle - 2.5 hours - 125 - 5 = 120 pages Correct

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Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of [#permalink]

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11 Jan 2016, 23:47

CounterSniper wrote:

HEARTOFWOLF wrote:

Thanks CounterSniper, one kudo for you. I did make a mistake

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Re: Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of [#permalink]

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13 Jan 2016, 01:03

Bunuel wrote:

50/20 = 2.5 from when Michelle started. So 8:30.
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Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of [#permalink]

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14 Dec 2018, 00:50

my approach:

@4:30 pm Ron starts reading from page 5.
@ 5:30 pm Ron has read 30+5 pages = 35 (M=0)
@6pm he would have read 35 + 30/2 = 50 pages (M will start now)
@ 7 pm he would have read 80 pages while M would've read 50
@8 pm R = 110 M= 100
@8:30pm R= (110 + 30/2) 125 M= (100 + 50/2) 125

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Re: Ron begins reading a book at 4: 30 p.m. and reads at a steady pace of [#permalink] 18 Jan 2020, 03:37

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