Sumukh19 wrote:
Bob can read 30 pages and Jane can read 40 pages in an hour. Bob starts with a novel at 4:30 PM and Jane starts with the same novel at 5:20 pm, then after how many minutes after 5:20 pm, will they start reading the same page?
Posted from my mobile deviceLet's start with a
word equation.
The point when both people begin reading the SAME page, we know that
both people have read the same number of pagesSo we can write:
number of pages Bob has read = number of pages Jane has readGiven: Bob starts reading at 4.30 pm, and Jane starts reading at 5.20 pmIn other words, Bob is given a 50-minute head start (aka a head start of 5/6 hours).
So, if we let
t = the amount of time, in hours, Jane spent reading, then....
t + 5/6 = the amount of time, in hours, Bob spent reading (since Bob gets to read for an additional 50 minutes)
Output = (rate)(time) Substitute values into the original word equation to get:
(30)(t + 5/6) = (40)(t)Expand the left side to get:
30t + 25 = 40tSubtract 30t from both sides of the equation:
25 = 10tSolve:
t = 25/10 = 2.5In other words, Jane's reading time = 2.5 hours.
Since Jane began reading at 5:20, the time at which they were both reading the same page = 5:20 + 2.5 hours = 5:20 + (
150 minutes)
Answer: 150