Final answer:
Larry drove 50 mph to the convention and 40 mph back home. The total drive time was 9 hours, and by setting up the equation with speeds and distances, and then solving for x, we can determine the speeds in each direction.
Step-by-step explanation:
To solve for Larry's speed in each direction, we use the formula distance = speed × time. Let's denote the speed on the way there as x mph and the speed on the way back as x - 10 mph. Since the distance in each direction is 200 miles, the time taken to travel to the convention is 200/x hours, and the time taken to travel back is 200/(x - 10) hours. The total driving time given is 9 hours, so we can set up the equation:
200/x + 200/(x - 10) = 9.
To solve this equation, we find a common denominator and solve for x. After simplifying, we get:
200(x - 10) + 200x = 9x(x - 10)
200x - 2000 + 200x = 9x^2 - 90x
400x - 2000 = 9x^2 - 90x
9x^2 - 490x + 2000 = 0
Using the quadratic formula or factoring, we find that x = 50 mph is a suitable solution (the other solution being negative and thus non-physical). Therefore, Larry drove 50 mph to the convention and 40 mph back home. The correct answer is (a) 50 mph there, 40 mph back.