2022 AMC 8 Problems/Problem 22
Contents
Problem
A bus takes minutes to drive from one stop to the next, and waits
minute at each stop to let passengers board. Zia takes
minutes to walk from one bus stop to the next. As Zia reaches a bus stop, if the bus is at the previous stop or has already left the previous stop, then she will wait for the bus. Otherwise she will start walking toward the next stop. Suppose the bus and Zia start at the same time toward the library, with the bus
stops behind. After how many minutes will Zia board the bus?
Solution 1
Initially, suppose that the bus is at Stop (starting point) and Zia is at Stop
We construct the following table of -minute intervals:
Note that Zia will wait for the bus after
minutes, and the bus will arrive
minutes later.
Therefore, the answer is
~MRENTHUSIASM
Solution 2
Since Zia will wait for the bus if the bus is at the previous stop, we can create an equation to solve for when the bus is at the previous stop. The bus travels of a stop per minute, and Zia travels
of a stop per minute. Now we create the equation,
(the
accounts for us wanting to find when the bus reaches the stop before Zia's). Solving, we find that
Now Zia has to wait
minutes for the bus to reach her, so our answer is
~kn07
Video Solution
https://www.youtube.com/watch?v=SFp4HaieEBg
~Mathematical Dexterity
Video Solution
https://youtu.be/Ij9pAy6tQSg?t=2111
~Interstigation
Video Solution
https://www.youtube.com/watch?v=m2D9W9LWUpU
See Also
2022 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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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