Difference between revisions of "2020 AMC 8 Problems/Problem 11"
Wuwang2002 (talk | contribs) (→Solution 1) |
|||
Line 58: | Line 58: | ||
We see that Naomi travels <math>6</math> miles in <math>\dfrac{1}{6}</math> of an hour. Thus, his speed is <math>36</math> mph. Maya's speed is <math>12</math> mph. The difference is <math>36 - 12 = \boxed{(\text{E}) 24}.</math> | We see that Naomi travels <math>6</math> miles in <math>\dfrac{1}{6}</math> of an hour. Thus, his speed is <math>36</math> mph. Maya's speed is <math>12</math> mph. The difference is <math>36 - 12 = \boxed{(\text{E}) 24}.</math> | ||
-[[User:A_mathemagician|A_MatheMagician]] | -[[User:A_mathemagician|A_MatheMagician]] | ||
+ | |||
+ | ==Video Solution== | ||
+ | https://youtu.be/y__IHWpXprY | ||
+ | |||
+ | ~savannahsolver | ||
==See also== {{AMC8 box|year=2020|num-b=10|num-a=12}} {{MAA Notice}} | ==See also== {{AMC8 box|year=2020|num-b=10|num-a=12}} {{MAA Notice}} |
Revision as of 18:16, 19 November 2020
Contents
Problem 11
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
We use the formula . Naomi's distance is
miles, and her time is
minutes, which is equivalent to
of an hour.
Since speed is distance over time, Naomi's speed is
mph.
Using the same process, Maya's speed is
mph. Subtracting those, we get an answer of
.
-wuwang2002
Solution 2
Notice that Naomi travels at a rate of miles every
minutes or
miles an hour. Maya travels at a rate of
miles every
minutes or
miles an hour. Hence, the answer is
.
-franzliszt
Solution 3
Notice that the difference between Maya's and Naomi's arrival time is 4 units on the graph, or twice as slow as Naomi. Since Naomi's time to go is minutes, their difference in speed is
~SweetMango77
Solution 4
We see that Naomi travels miles in
of an hour. Thus, his speed is
mph. Maya's speed is
mph. The difference is
-A_MatheMagician
Video Solution
~savannahsolver
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.