Harvey the wonder hamster can run

Question

\[3\dfrac{1}6 \text{ km}\] in

\[\dfrac{1}4\] hour. Harvey runs at a constant rate.
Find his average speed in kilometers per hour.

Answer 1

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.