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. $\newline$ $\square$ kilometers per hour

Full solution

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

\square

kilometers per hour

Convert to Improper Fraction: To find Harvey's average speed, we need to divide the distance he runs by the time it takes. So we'll take the distance, $3 \frac{1}{6}$ km, and divide it by the time, $\frac{1}{4}$ hour.
Divide by Reciprocal: First, let's convert the mixed number $3 \frac{1}{6}$ km to an improper fraction. That's $3 \times 6$ , which is $18$ , plus $1$ , which gives us $19$ . So, $3 \frac{1}{6}$ km is the same as $\frac{19}{6}$ km.
Multiply Fractions: Now, we divide $\frac{19}{6}$ km by $\frac{1}{4}$ hour. To divide by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{1}{4}$ is $\frac{4}{1}$ .
Simplify Result: So, we multiply $\frac{19}{6}\,\text{km}$ by $\frac{4}{1}$ to find Harvey's speed. That's $\frac{19}{6} \times \frac{4}{1}$ , which equals $\frac{76}{6}$ .
Convert to Mixed Number: Now we simplify $76/6$ . This can be reduced to $38/3$ by dividing both the numerator and the denominator by $2$ .
Convert to Mixed Number: Now we simplify $\frac{76}{6}$ . This can be reduced to $\frac{38}{3}$ by dividing both the numerator and the denominator by $2$ .Finally, we convert $\frac{38}{3}$ to a mixed number to make it easier to understand. $38$ divided by $3$ is $12$ with a remainder of $2$ , so Harvey's average speed is $12\frac{2}{3}$ kilometers per hour.