Distance between Sumter and Columbia is 48 miles, and there is a bridge crossing a river at the midpoint between the two towns. A man from Sumter and a man from Columbia start walking toward each other. The man who started in Sumter traveled uniformly with average speed 4 mph. The man from Columbia started an hour later, and in an attempt to make up lost time began jogging at 6 mph. After two hours, however, the Columbia man needed to rest for an hour before he could resume at the same pace. Where will the two men meet? Choose the correct choice.
A) On the Columbia side, 4 miles away from the bridge
B) On the Sumter side, 6 miles away from the bridge
C) On the Columbia side, 6 miles away from the bridge
D) On the Sumter side, 4 miles away from the bridge
E) On the bridge
Since the question asks where Sumter and Columbia men 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 the Sumter man is 4 mph and distance is 48 miles. So this means that A would take a total of   48/4= 
<gadget id="calculator">  48/4</gadget>
<output>12</output>
12 hours to cover the distance from Sumter to Columbia. So, if the Columbia man's speed were also 4, both men travel for 6 hours to meet in the middle.   Since we know the Columbia man started late, the rate for his first hour is 0, followed by two hours of 6 mph. The Columbia man then has to rest for an hour before continuing, so we know the pattern of 0, 6, 6, will continue. This means, for each three-hour period, the Columbia man will average 4 mph. Since the 6 hours before the Sumter man reached the bridge can be divided by 3, then both men will be traveling at the same average rate.   The correct answer is (On the bridge).
<result>E</result>
Distance between Sumter and Columbia is 48 miles, and there is a bridge crossing a river at the midpoint between the two towns. A man from Sumter and a man from Columbia start walking toward each other. The man who started in Sumter traveled uniformly with average speed 4 mph. The man from Columbia started an hour later, and in an attempt to make up lost time began jogging at 6 mph. After two hours, however, the Columbia man needed to rest for an hour before he could resume at the same pace. Where will the two men meet?