What Is the Average Reading Rate for Beth's Day?

In summary, Beth read 100 pages at the rate of 60 pages per hour; in the evening, when she was tired, she read another 100 pages at the rate of 40 pages per hour. Her average rate of reading for the day was 5 pages per hour.
  • #1
zak100
462
11
In the afternoon, Beth read 100 pages at the rate of 60 pages per hour; in the evening, when she was tired , she read another 100 pages at the rate of 40 pages per hour. What was her avg rate of reading for the day?

I can't understand why are we not finding avg time?

Homework Equations


S= v * t

The Attempt at a Solution


First find the total time.

Pages = 100, v= 60 pages per hour: S = v* t; 100= 60 *t; t= 100/60= 5/3

Pages = 100, v = 40pages per hour: S = v* t; 100= 40 *t; t= 100/40= 5/2

Total Time = 5/2 + 5/3= (15 + 10)/6 = 25/6

At this point my question is why are we not finding average time? We have to find average rate of reading. So we must find average time??
Some body please guide me.
Zulfi.
 
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  • #2
How long did it take her to read the first 100 pages? How long did it take her to read the second 100 pages? How many pages total? How much time total?
 
  • #3
zak100 said:
I can't understand why are we not finding avg time?
If you're thinking that the overall average time is the mean of the two averages, it isn't.

A classic problem that shows why this doesn't work is this one.

A man drives his car up a mile-long hill at a speed of 30 miles per hour. How fast does he need to go on the return trip downhill to average 60 miles per hour?

The naive (and incorrect) answer is 90 miles per hour.
 
  • #4
zak100 said:
Total Time = 5/2 + 5/3= (15 + 10)/6 = 25/6

At this point my question is why are we not finding average time? We have to find average rate of reading. So we must find average time??
Some body please guide me.
Zulfi.
You have found total time and the total number of pages is pretty straightforward. Average rate (pages/hour) is defined as (total pages) / (total hours). As Mark pointed out, it is not (rate1 + rate2)/2.
If you wanted to find average time, do you mean hours per page? That is the inverse of your rate (given in pages/hour).
So, you could get to the answer that way since the number of pages read is the same. avg. time = (time1+time2)/2. Your average rate would be 100 pages / average time.
A little algebra will show you that these equations are consistent. However, if you have different # of pages at each rate, the second method falls apart while the (total pages) / (total time) method still works.
 
  • #5
Thanks. Actually I was not able to understand the concept of average rate. Now its clear to me.

Zulfi.
 

What is the average rate of reading?

The average rate of reading is typically measured in words per minute (wpm) and can vary greatly depending on factors such as age, education level, and reading proficiency.

How is the average rate of reading determined?

The average rate of reading is determined by having an individual read a passage of text and tracking the number of words they read in a given amount of time. This is usually done through timed reading tests or through self-assessment.

What is the average rate of reading for adults?

The average rate of reading for adults is around 200-250 wpm. However, this can vary depending on the difficulty of the text and individual reading abilities.

Does the average rate of reading change with age?

Yes, as individuals age, their average rate of reading tends to decrease. This is due to factors such as declining eyesight, slower processing speed, and decreased reading habits.

Can the average rate of reading be improved?

Yes, the average rate of reading can be improved through various techniques such as speed reading exercises, increasing vocabulary, and improving comprehension skills. Consistent practice and exposure to a variety of reading materials can also help improve reading speed.

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