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Bob can read 30 pages and Jane can ready 40 pages in an hour. Bob starts reading a novel at 4.30 pm and Jane starts reading the same novel at 5.20 pm. then at what time will they be reading the same page?
A. 5.45 PM
B. 7.00 PM
C. 7.20 PM
D. 7.50 PM
E. 8.10 PM
Let'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 + (2 hours and 30 minutes) = 7:50 PM
Answer: D