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. Where will they meet each other?
Choose one
A) 12 miles away from A B) 12 miles away from B C) after 6 hours from start D) after 12 hours from start E) midway between A and B
Since the question asks where A and B will meet each other, we know the answer will involve distance and location.   In such questions, look for a 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.   The correct answer is (midway between A and B).
<result>E</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. Where will they meet each other?