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

[zak100]

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.

 

[phinds]

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?

 

[Mark44]

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.

 

[RUber]

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.

 

[zak100]

Thanks. Actually I was not able to understand the concept of average rate. Now its clear to me.

Zulfi.