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

`12(2)/(3)` kilometers per hour.

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(1)/(6)\text{ km}}{(1)/(4)\text{ hours}}}`

Convert mixed fractions into improper fractions:

`\text{Harvey's average speed}=\frac{(19)/(6)\text{ km}}{(1)/(4)\text{ hours}}}`

Using
`((a)/(b))/((c)/(d))=(a\cdot d)/(b\cdot c)`, we will get:

`\text{Harvey's average speed}=(19\cdot 4)/(6\cdot 1)\frac{\text{ km}}{\text{ hour}}`

`\text{Harvey's average speed}=(19\cdot 2)/(3)\frac{\text{ km}}{\text{ hour}}`

`\text{Harvey's average speed}=(38)/(3)\frac{\text{ km}}{\text{ hour}}`

`\text{Harvey's average speed}=12(2)/(3)\frac{\text{ km}}{\text{ hour}}`

Therefore, Harvey's average speed is
`12(2)/(3)` kilometers per hour.