Abigale, Wendel and Yanni are three contestants on Graham’s favorite game show. In one of the rounds of the game show the 3 contestants have a chance to spin a wheel up to two times in a row to try to get the highest possible sum without going over 100. The wheel that they spin is divided into 21 equal portions, each containing one element from the set of numbers containing 1 and all of the multiples of 5 less than or equal to 100.
Abigale goes first. If she spins the wheel twice, getting a 15 and a 50, what is the probability that on his first spin Wendel gets a number larger than Abigale’s sum? Express your answer as a common fraction.
Wendel spins a 10 on his first spin. If he spins the wheel a second time, what is the probability that the sum of his two spins will be a multiple of 4? Express your answer as a common fraction.
After his second spin, Wendel ended up with a sum of 50. This means Abigale was still in the lead. If Yanni spins a number greater than 65 on his first spin, he will not spin again. If he spins a number less than or equal to 65 he will spin again. What is the probability that Yanni ends up being the winner? Express your answer as a common fraction.
The solutions to this week's problems will be posted in the Archive on Monday, February 1st 2010.
Jean made a New Year’s resolution to get in shape. She decides to run for 30 minutes on Tuesdays, Thursdays, Saturdays and Sundays. If Jean plans to run at an average speed of 6 mph, how many miles will she run during the month of February 2010? After some consideration, Jean decides that it might be better to run at an average speed of 5.0 miles per hour on her first day of running in February and then increase her average speed by 0.1 miles per hour each day she runs. How many fewer miles will she run than if she were to run at an average speed of 6.0 mph each time she runs? By following the new plan, by what percent will Jean have increased her average speed from the first running day in February to the last running day in February?