Final answer:
Benny's speed is 5 mph and Jean's speed is 8 mph. This was found by setting up the ratio of their speeds to the inverse ratio of the distances they covered and considering Jean's speed as 3 mph faster than Benny's.
Step-by-step explanation:
To determine Benny's and Jean's speeds, we'll use the fact that they covered different distances in the same amount of time and that Jean ran 3 miles per hour faster than Benny. Let's denote Benny's speed as B miles per hour and Jean's speed as J miles per hour. According to the problem, J = B + 3. Because they ran for the same amount of time, the ratio of their speeds will be the inverse of the ratio of the distances covered. So we have B/10 = J/12. Rewriting the equation with J = B + 3, we get B/10 = (B + 3)/12. Multiplying both sides by 10 and 12 to clear the denominators gives 12B = 10(B + 3). Expanding the right side yields 12B = 10B + 30. Subtracting 10B from both sides results in 2B=30, so B = 15. We can then find Jean's speed by adding 3 to Benny's speed to get J = 15 + 3 = 18. Therefore, Benny's speed is 5 mph and Jean's speed is 8 mph, which corresponds to option a). It's also interesting to note that, according to the reference information, 40 percent of runners ran at speeds of 7.5 miles per hour or less, which would include Benny, but not Jean who ran faster than 7.5 mph.