The runner-up in a road race is given a reward that depends on the difference between his time and the winner's time. He is given 20 dollars for being one minute behind, 10 dollars for being one to two minutes behind, 5 dollars for being 2 to 6 minutes behind, and nothing otherwise. Given that the difference between his time and the winner's time is uniformly distributed between 0 and 12 minutes, find the mean and variance of the reward of the runner-up.