2025 AMC 8 Problems/Problem 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?
Solution 1
The first car, moving from town at
miles per hour, takes
minutes. The second car, traveling another
miles from town
, takes
minutes. The first car has traveled for 3 minutes or
th of an hour at
miles per hour when the second car has traveled 5 miles. The first car has traveled
miles from the previous
miles it traveled at
miles per hour. They have
miles left, and they travel at the same speed, so they meet
miles through, so they are
miles from town
.
~alwaysgonnagiveyouup