John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 2, 3, 4, 5, or 6 miles per hour and Amanda runs at a constant rate of 3, 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet? Choose the correct option:
A) 1/3 B) 2/5 C) 3/5 D) 4/25 E) 6/25
John will run farther if he runs at 6 mph and Amanda runs at 5 mph, 4 mph, or 3 mph.   In this case, P(John runs farther) = 1/5 * 3/5 = 3/25   John will run farther if he runs at 5 mph and Amanda runs at 4 mph or 3 mph.   In this case, P(John runs farther) = 1/5 * 2/5 = 2/25   John will run farther if he runs at 4 mph and Amanda runs at 3 mph.   In this case, P(John runs farther) = 1/5 * 1/5 = 1/25   Overall, P(John runs farther) = 3/25 + 2/25 + 1/25 = 6/25   The answer is 6/25.
<result>E</result>
John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 2, 3, 4, 5, or 6 miles per hour and Amanda runs at a constant rate of 3, 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet?