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, or 5 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 / 5 B) 2 / 5 C) 3 / 10 D) 3 / 20 E) 7 / 20

Rationale: 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 / 4 * 2 / 5 = 2 / 20 john will run farther if he runs at 4 mph and amanda runs at 3 mph . in this case , p ( john runs farther ) = 1 / 4 * 1 / 5 = 1 / 20 p ( john runs farther ) = 2 / 20 + 1 / 20 = 3 / 20 the answer is d .
Answer: D