Difference between revisions of "2020 AMC 8 Problems/Problem 11"
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− | ==Problem | + | ==Problem== |
After school, Maya and Naomi headed to the beach, <math>6</math> miles away. Maya decided to bike while Naomi took a bus. The graph below shows their journeys, indicating the time and distance traveled. What was the difference, in miles per hour, between Naomi's and Maya's average speeds? | After school, Maya and Naomi headed to the beach, <math>6</math> miles away. Maya decided to bike while Naomi took a bus. The graph below shows their journeys, indicating the time and distance traveled. What was the difference, in miles per hour, between Naomi's and Maya's average speeds? | ||
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<math>\textbf{(A) }6 \qquad \textbf{(B) }12 \qquad \textbf{(C) }18 \qquad \textbf{(D) }20 \qquad \textbf{(E) }24</math> | <math>\textbf{(A) }6 \qquad \textbf{(B) }12 \qquad \textbf{(C) }18 \qquad \textbf{(D) }20 \qquad \textbf{(E) }24</math> | ||
− | ==Solution== | + | ==Solution 1== |
+ | Naomi travels <math>6</math> miles in a time of <math>10</math> minutes, which is equivalent to <math>\dfrac{1}{6}</math> of an hour. Since <math>\text{speed} = \frac{\text{distance}}{\text{time}}</math>, her speed is <math>\frac{6}{\left(\frac{1}{6}\right)} = 36</math> mph. By a similar calculation, Maya's speed is <math>12</math> mph, so the answer is <math>36-12 = \boxed{\textbf{(E) }24}</math>. | ||
− | + | ==Solution 2 (variant of Solution 1)== | |
− | + | Naomi's speed of <math>6</math> miles in <math>10</math> minutes is equivalent to <math>6 \cdot 6 = 36</math> miles per hour, while Maya's speed of <math>6</math> miles in <math>30</math> minutes (i.e. half an hour) is equivalent to <math>6 \cdot 2 = 12</math> miles per hour. The difference is consequently <math>36-12=\boxed{\textbf{(E) }24}</math>. | |
− | + | ||
+ | ==Video Solution by WhyMath== | ||
+ | https://youtu.be/y__IHWpXprY | ||
+ | |||
+ | ~savannahsolver | ||
+ | |||
+ | ==Video Solution== | ||
+ | https://youtu.be/xjwDsaRE_Wo | ||
+ | |||
+ | ==See also== {{AMC8 box|year=2020|num-b=10|num-a=12}} | ||
+ | {{MAA Notice}} |
Latest revision as of 18:18, 26 February 2021
Contents
Problem
After school, Maya and Naomi headed to the beach, miles away. Maya decided to bike while Naomi took a bus. The graph below shows their journeys, indicating the time and distance traveled. What was the difference, in miles per hour, between Naomi's and Maya's average speeds?
Solution 1
Naomi travels miles in a time of minutes, which is equivalent to of an hour. Since , her speed is mph. By a similar calculation, Maya's speed is mph, so the answer is .
Solution 2 (variant of Solution 1)
Naomi's speed of miles in minutes is equivalent to miles per hour, while Maya's speed of miles in minutes (i.e. half an hour) is equivalent to miles per hour. The difference is consequently .
Video Solution by WhyMath
~savannahsolver
Video Solution
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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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