Distance between A and B is 54 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 3 mph. While the other man traveled with varying speeds as follows: In first hour his speed was 2 mph, in the second hour it was 2.25 mph, in the third hour it was 2.5 mph, and so on. How fast was B walking when the two men finally meet? Pick one:
A) 3 mph  B) 3.5 mph  C) 4 mph  D) 4.5 mph  E) 5 mph
Since the question is about speed, we know the answer will be in rate, which in this case is miles per hour.   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 3 mph and distance is 54 miles. So this means that A would take a total of   54/3= 
<gadget id="calculator">  54/3</gadget>
<output>18</output>
18 hours to cover the distance from A to B. So, if B's speed were also 3, 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: 2, 2.25, 2.5, 2.75, 3, 3.25, 3.5...   and since 3 is actually right in the middle of the 9 speeds, both A and B will end with same average speed, and will meet after 9 hours.   Once this is determined, see what the final speed of B (during the ninth hour) is. In this case, B's speed during the ninth hour was 4 mph, so the correct answer is (4 mph): 4 mph.
<result>C</result>
Distance between A and B is 54 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 3 mph. While the other man traveled with varying speeds as follows: In first hour his speed was 2 mph, in the second hour it was 2.25 mph, in the third hour it was 2.5 mph, and so on. How fast was B walking when the two men finally meet?