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How to Calculate Average Sailing Speed in Knots (39km in 3 Hours)
Mathematics
Grade 7 (Junior High School)
Question Content
Luca sailed 39km in 3 hours on a single journey. He wants to know his speed in knots. Use 1 knot = 2km/hour. (b) Work out the average speed Luca sailed on this journey. Give your answer in knots.
Correct Answer
6.5 knots
Detailed Solution Steps
1
Step 1: Calculate the average speed in km/h first using the formula for average speed: Average Speed = Total Distance ÷ Total Time. Substitute the values: 39 km ÷ 3 hours = 13 km/h.
2
Step 2: Convert the speed from km/h to knots using the given conversion factor (1 knot = 2 km/h). Divide the speed in km/h by 2: 13 km/h ÷ 2 = 6.5 knots.
Knowledge Points Involved
1
Average Speed Calculation
Average speed is defined as the total distance traveled divided by the total time taken, with the formula: Average Speed = Total Distance / Total Time. It is used to measure the overall rate of motion for a journey with constant or varying speed, and the units match the distance and time units used (e.g., km/h, m/s).
2
Unit Conversion
Unit conversion is the process of converting a quantity from one unit of measurement to another using a conversion factor. In this problem, the conversion factor is 1 knot = 2 km/h, so to convert km/h to knots, we divide the speed in km/h by the number of km/h per knot. This is used to switch between different standardized units for the same physical quantity.
3
Basic Division Operations
Basic division is an arithmetic operation that splits a quantity into equal parts or finds how many times one number fits into another. It is essential for calculating rates (like speed) and performing unit conversions, as seen in dividing total distance by time, and dividing km/h speed by the conversion factor.
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