I can read a 336-page book in 6 hours. Jayne can read a 144-page book in 3 hours. If I start reading a 5000-page book at noon and Jayne starts reading the same book at 10 AM, what time will it be when we are on the same page at the same time?

12:00 am midnight

Step-by-step explanation:

Given;

I can read a 336-page book in 6 hours.

My rate r1 = 336/6 pages per hour = 56 pages per hour

Jayne can read a 144-page book in 3 hours.

Jayne rate r2 = 144/3 = 48 pages per hour

If I start reading a 5000-page book at noon and Jayne starts reading the same book at 10 AM

Taking 10 am as the reference time.

Let x represent the time from 10 am at which they would both be on the same page.

For me;

Since i started by noon; 2 hours after 10 am

Time t1 = x-2

For Jayne;

She started by 10 am

Time t2 = x

For them to be on the same page they must have read the same number of pages;

Number of pages read = rate * time

r1 (t1) = r2 (t2)

Substituting the values;

56 (x-2) = 48 (x)

56x - 112 = 48x

x (56-48) = 112

x = 112 / (56-48)

x = 14 hours

Since 10 am is the reference, the time would be;

=10 am + x = 10 am + 14 hours

= 24:00

= 12:00 am midnight