Difference between revisions of "2019 AMC 8 Problems/Problem 16"
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The only option that is easily divisible by <math>55</math> is <math>110</math>. Which gives 2 hours of travel. And by the formula <math>\frac{15}{30} + \frac{110}{50} = \frac{5}{2}</math> | The only option that is easily divisible by <math>55</math> is <math>110</math>. Which gives 2 hours of travel. And by the formula <math>\frac{15}{30} + \frac{110}{50} = \frac{5}{2}</math> | ||
− | And <math>Average Speed</math> = <math>\frac{Total Distance}{Total Time}</math> | + | And <math>\text{Average Speed}</math> = <math>\frac{Total Distance}{Total Time}</math> |
Thus <math>\frac{125}{50} = \frac{5}{2}</math> | Thus <math>\frac{125}{50} = \frac{5}{2}</math> | ||
− | Both are equal and thus our answer <math>\boxed{\textbf{(D)}\ 110}</math> | + | Both are equal and thus our answer is <math>\boxed{\textbf{(D)}\ 110}.</math> |
~phoenixfire | ~phoenixfire |
Revision as of 17:39, 25 December 2019
Problem 16
Qiang drives miles at an average speed of miles per hour. How many additional miles will he have to drive at miles per hour to average miles per hour for the entire trip?
Solution 1(answer options)
The only option that is easily divisible by is . Which gives 2 hours of travel. And by the formula
And =
Thus
Both are equal and thus our answer is
~phoenixfire
Solution 2
Note that the average speed is simply the total distance over the total time. Let the number of additional miles he has to drive be Therefore, the total distance is and the total time (in hours) is We can set up the following equation: Simplifying the equation, we get Solving the equation yields so our answer is .
~twinemma
See Also
2019 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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 AJHSME/AMC 8 Problems and Solutions |
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