Racing

To determine the optimal route for three hockey players racing around a rink while passing two nets at the crease, we'll consider a few key factors:

1. Rink Dimensions: A standard ice hockey rink is 200 feet long and 85 feet wide. The goals (nets) are located at each end of the rink within the crease area, which is typically 6 feet wide and 4 feet deep.
2. Skating Speed: The players are skating at 15 miles per hour. We can convert this speed into feet per second for better calculations:
   • 15 miles per hour×5280 feet1 mile×1 hour3600 seconds≈22 feet per second15 \text{ miles per hour} \times \frac{5280 \text{ feet}}{1 \text{ mile}} \times \frac{1 \text{ hour}}{3600 \text{ seconds}} \approx 22 \text{ feet per second}15 miles per hour×1 mile5280 feet​×3600 seconds1 hour​≈22 feet per second.
3. Laps and Route: The players will skate 3 laps around the rink while needing to pass the two nets at the crease. The optimal route should minimize the distance traveled while still allowing them to effectively navigate around the nets.

Calculation of Distance

Let's break down the distance:

1. Perimeter of the Rink: The perimeter of a standard hockey rink can be calculated as follows: Perimeter=2×(length+width)=2×(200 ft+85 ft)=570 ft\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (200 \text{ ft} + 85 \text{ ft}) = 570 \text{ ft}Perimeter=2×(length+width)=2×(200 ft+85 ft)=570 ft
2. Total Distance for 3 Laps: Total Distance=3×Perimeter=3×570 ft=1710 ft\text{Total Distance} = 3 \times \text{Perimeter} = 3 \times 570 \text{ ft} = 1710 \text{ ft}Total Distance=3×Perimeter=3×570 ft=1710 ft

Optimal Skating Path

To optimize the route, players should consider:

• Avoiding the Crease: When approaching the nets, they should aim to minimize any detours by skirting around the crease effectively.
• Staying Close to the Boards: Staying close to the boards may reduce the distance slightly compared to cutting through the middle.

Summary of Optimal Strategy

1. Initial Lap: Start at the goal line, skate toward the nearest corner, round it, and continue to the opposite corner.
2. Pass the Nets: As they approach the crease, they should keep their momentum by rounding the crease while minimizing the angle.
3. Stay Close to the Boards: Maintain close proximity to the boards when approaching turns, which can help maintain speed and efficiency.

Speed Calculation

To calculate how long it takes to complete the race:

1. Time for 3 laps: Time=Total DistanceSpeed=1710 ft22 ft/sec≈77.73 seconds\text{Time} = \frac{\text{Total Distance}}{\text{Speed}} = \frac{1710 \text{ ft}}{22 \text{ ft/sec}} \approx 77.73 \text{ seconds}Time=SpeedTotal Distance​=22 ft/sec1710 ft​≈77.73 seconds

Conclusion

The best route around the rink involves:

• Starting from one net, rounding the corners while staying close to the boards.
• Passing the crease without significant detours, minimizing time and distance.
• The estimated time to complete 3 laps is approximately 77.73 seconds at a consistent speed of 15 miles per hour.

These strategies should give the players a competitive edge in their race!