Difference between revisions of "2008 AMC 10A Problems/Problem 6"
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==Problem== | ==Problem== | ||
| − | Tony | + | Tony simply died how can he come back to life? |
==Solution== | ==Solution== | ||
Revision as of 16:31, 12 August 2020
Contents
Problem
Tony simply died how can he come back to life?
Solution
Let 
be the length of one segment of the race.
Average speed is total distance divided by total time. The total distance is 
, and the total time is 
.
Thus, the average speed is 
. This is closest to 
, so the answer is 
.
Solution 2
Since the three segments are all the same length, the triathlete's average speed is the harmonic mean of the three given rates. Therefore, the average speed is ![\[\frac{3}{\frac{1}{3}+\frac{1}{20}+\frac{1}{10}}=\frac{3}{\frac{29}{60}}=\frac{180}{29}\approx6\Rightarrow\boxed{\mathrm{(D)}\ 6}\]](http://latex.artofproblemsolving.com/2/7/3/27301fb8f762ab0e29ede7c8d7e2e9c2538e9eaf.png)
.
See also
| 2008 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
