Harvey the wonder hamster can run
\[3\dfrac{1}6 \text{ km}\] in
\[\dfrac{1}4\] hour. Harvey runs at a constant rate.
Find his average speed in kilometers per hour.
To find Harvey the wonder hamster's average speed, we need to divide the distance he ran by the time it took him to run that distance.
Harvey ran \(3\dfrac{1}{6}\) kilometers in \(\dfrac{1}{4}\) hour.
First, let's convert the mixed number into an improper fraction:
\[3\dfrac{1}{6} = \frac{(3 \times 6) + 1}{6} = \frac{18 + 1}{6} = \frac{19}{6}\]
Now we can calculate the average speed by dividing the distance by the time:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{19}{6} \text{ km}}{\frac{1}{4} \text{ hour}}\]
We can simplify this by multiplying by the reciprocal of the time fraction:
\[ \text{Speed} = \frac{19}{6} \text{ km} \times \frac{4}{1} \text{ hour}^{-1}\]
\[ \text{Speed} = \frac{19 \times 4}{6} \text{ km/hr} \]
\[ \text{Speed} = \frac{76}{6} \text{ km/hr} \]
To further simplify the fraction:
\[ \text{Speed} = 12\dfrac{4}{6} \text{ km/hr} \]
Since \(4/6\) can be reduced to \(2/3\):
\[ \text{Speed} = 12 \dfrac{2}{3} \text{ km/hr} \]
So, Harvey the wonder hamster's average speed is \(12 \dfrac{2}{3}\) kilometers per hour.