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Harvey the wonder hamster can run 3(1)/(6)km in (1)/(4) hour. Harvey runs at a constant rate. Find his average speed in kilometers per hour. kilometers per hour

Harvey the wonder hamster can run 316 km 3 \frac{1}{6} \mathrm{~km} in 14 \frac{1}{4} hour. Harvey runs at a constant rate.\newlineFind his average speed in kilometers per hour.\newlinekilometers per hour

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Q. Harvey the wonder hamster can run 316 km 3 \frac{1}{6} \mathrm{~km} in 14 \frac{1}{4} hour. Harvey runs at a constant rate.\newlineFind his average speed in kilometers per hour.\newlinekilometers per hour
  1. Identify values: Identify the given values.\newlineHarvey runs 3(16)3(\frac{1}{6}) km in (14)(\frac{1}{4}) hour.\newlineConvert the mixed number to an improper fraction for easier calculation.\newline3(16)3(\frac{1}{6}) km = (3×6+1)/6(3 \times 6 + 1)/6 km = (18+1)/6(18 + 1)/6 km = 196\frac{19}{6} km.
  2. Calculate average speed: Calculate the average speed using the formula.\newlineAverage speed = Total distance / Total time\newlineHere, Total distance = 196\frac{19}{6} km and Total time = 14\frac{1}{4} hour.
  3. Perform division: Perform the division to find the average speed.\newlineAverage speed = (196)(\frac{19}{6}) km ÷\div (14)(\frac{1}{4}) hour\newlineTo divide by a fraction, multiply by its reciprocal.\newlineAverage speed = (196)(\frac{19}{6}) km ×\times (41)(\frac{4}{1}) hour−1^{-1}
  4. Multiply numerators and denominators: Multiply the numerators and denominators.\newlineAverage speed = (19×4)/(6×1)(19 \times 4) / (6 \times 1) km/hour\newlineAverage speed = 76/676/6 km/hour
  5. Simplify fraction: Simplify the fraction if possible.\newline766\frac{76}{6} km/hour can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 22.\newlineAverage speed = (76÷26÷2)\left(\frac{76 \div 2}{6 \div 2}\right) km/hour\newlineAverage speed = 383\frac{38}{3} km/hour
  6. Convert to mixed number: Convert the improper fraction to a mixed number if necessary. 383\frac{38}{3} km/hour = 12(23)12\left(\frac{2}{3}\right) km/hour

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