Davey reads 45 pages in an hour. Sally reads 55 pages in an hour. If Davey begins to at 2pm and Sally starts to read at 2:40pm, at what time will they be reading the same exact page?
Sally reads 10 pp/hr faster than Davey.
Davey gets a 2/3 hour head start, in which time he reads 2/3 * 45 pp = 30 pp
So, it will take Sally 3 hours to catch up, putting the time at 5:40 pm.
The answer would be "Sally will take 3 hours to catch up with Davey."
To find out when Davey and Sally will be reading the same exact page, we need to determine their reading speeds and calculate the time it takes for them to read the same number of pages.
Davey reads 45 pages in an hour, so his reading speed is 45 pages per hour. Sally reads 55 pages in an hour, so her reading speed is 55 pages per hour.
Since Davey started reading at 2 pm, we need to calculate the time it takes for him to read a certain number of pages. Let's call that time 't'. We can use the formula:
t = number of pages / reading speed
For Davey, this becomes:
t = number of pages / 45
Sally, on the other hand, started reading at 2:40 pm. This means she started 40 minutes later than Davey. Remember that 1 hour is equal to 60 minutes. So, 40 minutes is equal to 40/60 = 2/3 of an hour.
To calculate Sally's reading time, we multiply t by (45/55) since her reading speed is 55 pages per hour:
t = (45/55) * (number of pages / 55)
Now we set both equations equal to each other and solve for t to find out when they will be reading the same number of pages:
number of pages / 45 = (45/55) * (number of pages / 55)
Simplifying this equation, we get:
55 * number of pages = 45 * (45/55) * number of pages
After canceling out the "number of pages" terms, we get:
55 = (45/55) * 45
Now, we can solve for (45/55) * 45 to find the number of pages they will be reading:
(45/55) * 45 = 36.8181818181...
Rounded to the nearest whole number, they will be reading 37 pages at the same time.
Now, we plug this value back into either of the original equations to find the time it takes for Davey or Sally to read 37 pages. Let's use Davey's equation:
t = number of pages / 45
t = 37 / 45
Calculating this, we find that it takes approximately 0.822 hours for Davey to read 37 pages.
Since Davey started reading at 2 pm, we add 0.822 hours to 2 pm to find the time when they will be reading the same exact page:
2 pm + 0.822 hours = 2:49 pm (rounded to the nearest minute)
Therefore, Davey and Sally will be reading the same exact page at around 2:49 pm.