Difference between revisions of "2021 AMC 10A Problems/Problem 6"
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==Problem== | ==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 <math>4</math> miles per hour. Halfway to the tower, the trail becomes really steep, and Chantal slows down to <math>2</math> miles per hour. After reaching the tower, she immediately turns around and descends the steep part of the trail at <math>3</math> miles per hour. She meets Jean at the halfway point. What was Jean's average speed, in miles per hour, until they | + | 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 <math>4</math> miles per hour. Halfway to the tower, the trail becomes really steep, and Chantal slows down to <math>2</math> miles per hour. After reaching the tower, she immediately turns around and descends the steep part of the trail at <math>3</math> miles per hour. She meets Jean at the halfway point. What was Jean's average speed, in miles per hour, until they meet? |
<math>\textbf{(A)} ~\frac{12}{13} \qquad\textbf{(B)} ~1 \qquad\textbf{(C)} ~\frac{13}{12} \qquad\textbf{(D)} | <math>\textbf{(A)} ~\frac{12}{13} \qquad\textbf{(B)} ~1 \qquad\textbf{(C)} ~\frac{13}{12} \qquad\textbf{(D)} |
Revision as of 06:34, 7 November 2022
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 trailhead to the fire tower, where
When Chantal meets Jean, the two have traveled for
hours. At that point, Jean has traveled for
miles, so his average speed is
miles per hour.
~MRENTHUSIASM
Solution 2 (Specified Distance)
We will follow the same template as shown in Solution 1, except that we will replace with a convenient constant.
Let miles be the distance from the trailhead to the fire tower. When Chantal meets Jean, the two have traveled for
hours. At that point, Jean has traveled for
miles, so his average speed is
miles per hour.
~MRENTHUSIASM
Video Solution 1 (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 4 (by TheBeautyofMath)
~IceMatrix
Video Solution by The Learning Royal
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.