2025 AMC 8 Problem 19
Attempt Problem 19 of the 2025 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2025 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
Two towns, and are connected by a straight road, miles long. Traveling from town to town the speed limit changes every miles: from to to miles per hour (mph). Two cars, one at town and one at town start moving toward each other at the same time. They drive at exactly the speed limit in each portion of the road. How far from town in miles, will the two cars meet?
Answer: D
Small hint:
Find when each car reaches the middle -mile section
Big hint:
Once both cars are in the middle section, their speeds are equal
Video solution:
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Written solution:
Think of the road as having three sections: left, middle, and right. Each section is miles long.
The car from reaches the middle section in hours.
The car from reaches the middle section in hours. By that time, the car from has already driven in the middle section for hours. During this time, that car from has traveled miles in the middle section.
That leaves miles between the two cars in the middle section.
At that moment, the car from is miles from
Since the cars drive at the same speed of mph in the middle section, they meet after each driving more miles. This takes the car from a total distance of miles, which is choice D.
Problem 19 in other years
- 1985 AMC 8
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