A common unit for speed used in sailing is the knot (nautical miles per hour). A nautical mile is about 1.15 regular miles. Calculate how much further (in feet) a boat moving at 22 knots will travel in 5 minutes compared to a car moving at 22 mph during the same time.
The Correct Answer and Explanation is :
A boat moving at 22 knots will travel approximately 1,452 feet further than a car moving at 22 miles per hour over a 5-minute period.
Explanation:
- Speed Conversion:
- A knot is a unit of speed used in nautical contexts, where 1 knot equals 1 nautical mile per hour.
- A nautical mile is approximately 1.15 regular miles. Therefore, to convert 22 knots to miles per hour, we multiply by 1.15:
[
22 \, \text{knots} \times 1.15 = 25.3 \, \text{miles per hour}
]
This means the boat is moving at 25.3 miles per hour.
- Distance Traveled:
- The formula for distance is:
[
\text{Distance} = \text{Speed} \times \text{Time}
] - Boat’s Distance:
The boat is traveling at 25.3 mph. Over 5 minutes (which is (\frac{5}{60}) hours), the boat will travel:
[
25.3 \, \text{miles per hour} \times \frac{5}{60} \, \text{hours} = 2.1083 \, \text{miles}
]
Converting this to feet (1 mile = 5280 feet):
[
2.1083 \, \text{miles} \times 5280 \, \text{feet} = 11,138 \, \text{feet}
] - Car’s Distance:
The car is traveling at 22 mph. Over 5 minutes:
[
22 \, \text{miles per hour} \times \frac{5}{60} \, \text{hours} = 1.8333 \, \text{miles}
]
Converting to feet:
[
1.8333 \, \text{miles} \times 5280 \, \text{feet} = 9670 \, \text{feet}
]
- Difference in Distance:
The difference in distance traveled between the boat and the car is:
[
11,138 \, \text{feet} – 9,670 \, \text{feet} = 1,452 \, \text{feet}
]
Thus, the boat travels 1,452 feet further than the car over the same 5-minute period.