Difference between revisions of "2022 AMC 8 Problems/Problem 22"
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We construct the following table of <math>5</math>-minute intervals: | We construct the following table of <math>5</math>-minute intervals: | ||
| + | <cmath>\begin{array}{c||c|c} | ||
| + | & & \\ [-2.5ex] | ||
| + | \textbf{Time} & \textbf{Bus's Location} & \textbf{Zia's Location} \\ [0.5ex] | ||
| + | \hline | ||
| + | & & \\ [-2ex] | ||
| + | \boldsymbol{5} \ \textbf{Minutes} & \text{Stop} \ 2 \ \text{(Boarding)} & \text{Stop} \ 4 \\ | ||
| + | \boldsymbol{10} \ \textbf{Minutes} & \text{Midpoint of Stops} \ 3 \ \text{and} \ 4 & \text{Stop} \ 5 \\ | ||
| + | \boldsymbol{15} \ \textbf{Minutes} & \text{Stop} \ 5 \ \text{(Leaving)} & \text{Stop} \ 6 | ||
| + | \end{array}</cmath> | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2022|num-b=21|num-a=23}} | {{AMC8 box|year=2022|num-b=21|num-a=23}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 23:17, 28 January 2022
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
Initially, suppose that the bus is at Stop 
(starting point) and Zia is at Stop 
We construct the following table of -minute intervals:
![\[\begin{array}{c||c|c} & & \\ [-2.5ex] \textbf{Time} & \textbf{Bus's Location} & \textbf{Zia's Location} \\ [0.5ex] \hline & & \\ [-2ex] \boldsymbol{5} \ \textbf{Minutes} & \text{Stop} \ 2 \ \text{(Boarding)} & \text{Stop} \ 4 \\ \boldsymbol{10} \ \textbf{Minutes} & \text{Midpoint of Stops} \ 3 \ \text{and} \ 4 & \text{Stop} \ 5 \\ \boldsymbol{15} \ \textbf{Minutes} & \text{Stop} \ 5 \ \text{(Leaving)} & \text{Stop} \ 6 \end{array}\]](http://latex.artofproblemsolving.com/5/7/a/57a2e5db3443f9a3f831f457904e306dd584804c.png)
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
