Difference between revisions of "2008 AMC 10B Problems/Problem 25"
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The truck always moves for <math>20</math> seconds, then stands still for <math>30</math>. In these <math>50</math> seconds, the truck will drive <math>200+0=200</math> meters. In those <math>50</math> seconds Michael will walk <math>250</math> meters. So ultimately Michael will be way too far ahead of the truck for any more meetings to happen. | The truck always moves for <math>20</math> seconds, then stands still for <math>30</math>. In these <math>50</math> seconds, the truck will drive <math>200+0=200</math> meters. In those <math>50</math> seconds Michael will walk <math>250</math> meters. So ultimately Michael will be way too far ahead of the truck for any more meetings to happen. | ||
− | The movement of Michael and the truck is plotted below: Michael in blue, the truck in red. We can easily verify that indeed there will be <math>\boxed{5}</math> | + | The movement of Michael and the truck is plotted below: Michael in blue, the truck in red. We can easily verify that indeed there will be <math>\boxed{5}</math> meetings: (the graph of the truck should start 200 units higher) |
* Michael will catch and overtake the truck while it is standing at the first pail. | * Michael will catch and overtake the truck while it is standing at the first pail. | ||
* The truck will start moving again and on its way to the second pail it will overtake Michael. | * The truck will start moving again and on its way to the second pail it will overtake Michael. |
Revision as of 19:24, 31 January 2009
Problem
Michael walks at the rate of feet per second on a long straight path. Trash pails are located every feet along the path. A garbage truck travels at feet per second in the same direction as Michael and stops for seconds at each pail. As Michael passes a pail, he notices the truck ahead of him just leaving for the next pail. How many times will Michael and the truck meet?
Solution
The truck always moves for seconds, then stands still for . In these seconds, the truck will drive meters. In those seconds Michael will walk meters. So ultimately Michael will be way too far ahead of the truck for any more meetings to happen.
The movement of Michael and the truck is plotted below: Michael in blue, the truck in red. We can easily verify that indeed there will be meetings: (the graph of the truck should start 200 units higher)
- Michael will catch and overtake the truck while it is standing at the first pail.
- The truck will start moving again and on its way to the second pail it will overtake Michael.
- While the truck is standing at the second pail, Michael will walk past it.
- The last meeting will occur exactly when both Michael and the truck arrive at the same time to the third pail.
See also
2008 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last Question | |
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 |