Questions: An economy consists of three workers: Jake; Nick, and Tim. Each works 10 hours a day and can produce two services: mowing lawns and washing cars. In an hour, Jake can either mow 1 lawn or wash 1 car; Nick can either mow 1 lawn or wash 2 cars; and Tim can either mow 2 lawns or wash 1 car. For each of the scenarios listed in the following table, determine how many lawns will be mowed and how many cars will be washed per day and enter these values into the corresponding row. All three spend all their time mowing lawns. (A) All three spend all their time washing cars. (B) All three spend half their time on each activity. (C) Jake spends half his time on each activity, while Nick only washes cars and Tim only mows lawns. (D)

To solve this problem, we need to calculate the number of lawns mowed and cars washed for each scenario based on the productivity of each worker and the time they allocate to each activity.

• Jake: 10 hours mowing = 10 lawns
• Nick: 10 hours mowing = 10 lawns
• Tim: 10 hours mowing = 20 lawns

Total Lawns Mowed: 10 + 10 + 20 = 40 lawns
Total Cars Washed: 0 cars

• Jake: 10 hours washing = 10 cars
• Nick: 10 hours washing = 20 cars
• Tim: 10 hours washing = 10 cars

Total Lawns Mowed: 0 lawns
Total Cars Washed: 10 + 20 + 10 = 40 cars

• Jake: 5 hours mowing = 5 lawns, 5 hours washing = 5 cars
• Nick: 5 hours mowing = 5 lawns, 5 hours washing = 10 cars
• Tim: 5 hours mowing = 10 lawns, 5 hours washing = 5 cars

Total Lawns Mowed: 5 + 5 + 10 = 20 lawns
Total Cars Washed: 5 + 10 + 5 = 20 cars

• Jake: 5 hours mowing = 5 lawns, 5 hours washing = 5 cars
• Nick: 10 hours washing = 20 cars
• Tim: 10 hours mowing = 20 lawns

Total Lawns Mowed: 5 + 20 = 25 lawns
Total Cars Washed: 5 + 20 = 25 cars

\[ \begin{array}{|l|c|c|} \hline \text{Scenario} & \text{Lawns Mowed} & \text{Cars Washed} \\ \hline \text{All three spend all their time mowing lawns. (A)} & 40 & 0 \\ \text{All three spend all their time washing cars. (B)} & 0 & 40 \\ \text{All three spend half their time on each activity. (C)} & 20 & 20 \\ \text{Jake spends half his time on each activity, while Nick only washes cars and Tim only mows lawns. (D)} & 25 & 25 \\ \hline \end{array} \]