Question

Harvey the wonder hamster can run 3 1 6 km 3 6 1 ​ km3, start fraction, 1, divided by, 6, end fraction, start text, space, k, m, end text in 1 4 4 1 ​ start fraction, 1, divided by, 4, end fraction hour. Harvey runs at a constant rate. Find his average speed in kilometers per hour.

Answer 1

Answer:

$12\frac{2}{3}$ kilometers per hour.

Step-by-step explanation:

We have been given that Harvey the wonder hamster can run 3 1/6 km in 1/4 hour. We are asked to find Harvey's average speed in kilometers per hour.

To find Harvey's average speed, we will divide total distance by total time taken.

$\text{Average speed}=\frac{\text{Total distance traveled}}{\text{Total time}}$

$\text{Harvey's average speed}=\frac{3\frac{1}{6}\text{ km}}{\frac{1}{4}\text{ hours}}}$

Convert mixed fractions into improper fractions:

$\text{Harvey's average speed}=\frac{\frac{19}{6}\text{ km}}{\frac{1}{4}\text{ hours}}}$

Using $\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}$, we will get:

$\text{Harvey's average speed}=\frac{19\cdot 4}{6\cdot 1}\frac{\text{ km}}{\text{ hour}}$

$\text{Harvey's average speed}=\frac{19\cdot 2}{3}\frac{\text{ km}}{\text{ hour}}$

$\text{Harvey's average speed}=\frac{38}{3}\frac{\text{ km}}{\text{ hour}}$

$\text{Harvey's average speed}=12\frac{2}{3}\frac{\text{ km}}{\text{ hour}}$

Therefore, Harvey's average speed is $12\frac{2}{3}$ kilometers per hour.