Nick, Joey, Beki, and Carmen ran in the town's annual road race. Each person had a different jersey number {2, 13, 20, and 34} and finished in a different amount of time {10 minutes, 11 minutes, 12 minutes, and 14 minutes}. Use the information and deductive reasoning to determine each person's jersey number and race time.

•the runner with the lowest jersey number also ran the slowest time

• Nick's jersey number is 18 greater than Carmen's.

•Of the four runners, a man had the fastest finishing time.

• The sum of the digits on Beki's jersey number is 7

•Nick finished exactly 2 minutes faster than Beki.

Beki's jersey number is 34. She last 12 minutes

Nick's jersey number is 20. He last 10 minutes

Carmen's jersey number is 2. She last 14 minutes

Joey's jersey number is 13. He last 11 minutes

Step-by-step explanation:

• The sum of the digits on Beki's jersey number is 7. Therefore, Beki's number is necessarily 34 (3+4 = 7)

• Nick's jersey number is 18 greater than Carmen's. Therefore, Nick's jersey number is 20 and Carmen's jersey number is 2 (2 + 18 = 20). If Carmen's jersey number was 13, 13+18 = 31 which is not included in the options. If it was 20, 20+18 = 38 is not included either.

• From previous items, Joey's jersey number is 13

• The runner with the lowest jersey number also ran the slowest time. Therefore, Carmen last 14 minutes

• Nick finished exactly 2 minutes faster than Beki. Therefore, Nick's time is 10 minutes and Beki's time is 12 minutes, because from the remaining options (10, 11 and 12) this is the only combination 2 minutes apart.

• From previous items, Joey's time is 11 minutes