Distance between A and B is 36 miles. Two men started walking from A and B at the same time towards each other. The person who started from A traveled uniformly with average speed 2 mph. While the other man traveled with varying speeds as follows: In first hour his speed was 1 mph, in the second hour it was 1.25 mph, in the third hour it was 1.5 mph, and so on. When will they meet each other?	Pick one
A) 12 miles away from A	B) 12 miles away from B	C) after 6 hours from start	D) after 9 hours from start	E) after 12 hours from start
Since the question is asking when A and B will meet each other, the answer will be one involving time elapsed.   In such questions, look for the symmetrical situation to find a rough estimate or range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same.   Here the average speed of A (assuming guy who starts from A is A) is 2 mph and distance is 36 miles. So this means that A would take a total of   36/2= 
<gadget id="calculator">  36/2</gadget>
<output>18</output>
18 hours to cover the distance from A to B. So, if B's speed were also 2, both A and B would travel for 9 hours to meet in the middle.   B has uniform speed per hour so its average will be the simple average of all speeds: 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5...   and 2 is actually right in the middle of the 9 speeds, implying both A and B have the same average speed.   Since 2 is actually right in the middle of the 9 speeds, this implies both A and B will have the same average speed.   So the correct answer is (D): A and B will meet after 9 hours (midway between A and B.)   Had it been determined that B's average speed was more than 2 then that would indicate A and B would meet closer to point A and will take less than 9 hours and so on...   The correct answer is (after 9 hours from start).
<result>D</result>
Distance between A and B is 36 miles. Two men started walking from A and B at the same time towards each other. The person who started from A traveled uniformly with average speed 2 mph. While the other man traveled with varying speeds as follows: In first hour his speed was 1 mph, in the second hour it was 1.25 mph, in the third hour it was 1.5 mph, and so on. When will they meet each other?