Difference between revisions of "2021 AMC 10A Problems/Problem 6"
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== Solution 2 (Convenient Distance) == | == Solution 2 (Convenient Distance) == | ||
− | <b>We use the same template as shown in Solution 1, except that we replace <math>\ | + | <b>We use the same template as shown in Solution 1, except that we replace <math>\boldsymbol{d}</math> with a concrete number.</b> |
Let <math>24</math> miles be the distance from the start to the fire tower. When Chantal meets Jean, she travels for <cmath>\frac{12}{4} + \frac{12}{2}+\frac{12}{3}=3+6+4=13</cmath> hours. Jean also has traveled for <math>13</math> hours, and he travels for <math>12</math> miles. So, his average speed is <math>\boxed{\textbf{(A)} ~\frac{12}{13}}</math> miles per hour. | Let <math>24</math> miles be the distance from the start to the fire tower. When Chantal meets Jean, she travels for <cmath>\frac{12}{4} + \frac{12}{2}+\frac{12}{3}=3+6+4=13</cmath> hours. Jean also has traveled for <math>13</math> hours, and he travels for <math>12</math> miles. So, his average speed is <math>\boxed{\textbf{(A)} ~\frac{12}{13}}</math> miles per hour. |
Revision as of 20:18, 22 February 2021
Contents
Problem
Chantal and Jean start hiking from a trailhead toward a fire tower. Jean is wearing a heavy backpack and walks slower. Chantal starts walking at miles per hour. Halfway to the tower, the trail becomes really steep, and Chantal slows down to
miles per hour. After reaching the tower, she immediately turns around and descends the steep part of the trail at
miles per hour. She meets Jean at the halfway point. What was Jean's average speed, in miles per hour, until they meet?
Solution 1 (Generalized Distance)
Let miles be the distance from the start to the fire tower. When Chantal meets Jean, she has traveled for
hours. Jean also has traveled for
hours, and he travels for
miles. So, his average speed is
miles per hour.
~MRENTHUSIASM
Solution 2 (Convenient Distance)
We use the same template as shown in Solution 1, except that we replace with a concrete number.
Let miles be the distance from the start to the fire tower. When Chantal meets Jean, she travels for
hours. Jean also has traveled for
hours, and he travels for
miles. So, his average speed is
miles per hour.
~MRENTHUSIASM
Video Solution (Using Speed, Time, Distance)
~ pi_is_3.14
Video Solution 2(Simple and Quick)
~ Education, the Study of Everything
Video Solution 3
~savannahsolver
Video Solution by TheBeautyofMath
~IceMatrix
See Also
2021 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.