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

Identify values: Identify the given values. Harvey runs 3(1/6) km in (1/4) hour. Convert the mixed number to an improper fraction for easier calculation. 3(1/6) km = (3 * 6 + 1)/6 km = (18 + 1)/6 km = 19/6 km.Calculate average speed: Calculate the average speed using the formula. Average speed = Total distance / Total time Here, Total distance = 19/6 km and Total time = 1/4 hour.Perform division: Perform the division to find the average speed. Average speed = (19/6) km ÷ (1/4) hour To divide by a fraction, multiply by its reciprocal. Average speed = (19/6) km × (4/1) hour⁻¹Multiply numerators and denominators: Multiply the numerators and denominators. Average speed = (19 * 4) / (6 * 1) km/hour Average speed = 76/6 km/hourSimplify fraction: Simplify the fraction if possible. 76/6 km/hour can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. Average speed = (76 ÷ 2) / (6 ÷ 2) km/hour Average speed = 38/3 km/hourConvert to mixed number: Convert the improper fraction to a mixed number if necessary. 38/3 km/hour = 12(2/3) km/hour

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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 $3 \frac{1}{6} \mathrm{~km}$ in $\frac{1}{4}$ hour. Harvey runs at a constant rate. $\newline$ Find his average speed in kilometers per hour. $\newline$ kilometers per hour

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Q. Harvey the wonder hamster can run

3 \frac{1}{6} \mathrm{~km}

\frac{1}{4}

hour. Harvey runs at a constant rate.

\newline

Find his average speed in kilometers per hour.

\newline

kilometers per hour

Identify values: Identify the given values. $\newline$ Harvey runs $3(\frac{1}{6})$ km in $(\frac{1}{4})$ hour. $\newline$ Convert the mixed number to an improper fraction for easier calculation. $\newline$ $3(\frac{1}{6})$ km = $(3 \times 6 + 1)/6$ km = $(18 + 1)/6$ km = $\frac{19}{6}$ km.
Calculate average speed: Calculate the average speed using the formula. $\newline$ Average speed = Total distance / Total time $\newline$ Here, Total distance = $\frac{19}{6}$ km and Total time = $\frac{1}{4}$ hour.
Perform division: Perform the division to find the average speed. $\newline$ Average speed = $(\frac{19}{6})$ km $\div$ $(\frac{1}{4})$ hour $\newline$ To divide by a fraction, multiply by its reciprocal. $\newline$ Average speed = $(\frac{19}{6})$ km $\times$ $(\frac{4}{1})$ hour $^{-1}$
Multiply numerators and denominators: Multiply the numerators and denominators. $\newline$ Average speed = $(19 \times 4) / (6 \times 1)$ km/hour $\newline$ Average speed = $76/6$ km/hour
Simplify fraction: Simplify the fraction if possible. $\newline$ $\frac{76}{6}$ km/hour can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ Average speed = $\left(\frac{76 \div 2}{6 \div 2}\right)$ km/hour $\newline$ Average speed = $\frac{38}{3}$ km/hour
Convert to mixed number: Convert the improper fraction to a mixed number if necessary. $\frac{38}{3}$ km/hour = $12\left(\frac{2}{3}\right)$ km/hour