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

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

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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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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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.
-----------------------------------------
Kudo me if my answer is good
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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

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

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

Thanks CounterSniper, one kudo for you. I did make a mistake
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50/20 = 2.5 from when Michelle started. So 8:30.
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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

I made a timeline:

Time: 1,5h-------2,5h-------3,5h----4h
R ---page 45 -----75--------105-----120
M---page -5 -----45--------95------120