Question

A runner runs 4777 ft in 7.27 minutes. What is the runners average speed in miles per hour?

Answer 1

Step 1 - Converting the units

Note that the exercise requires you to answer in units of miles/hour, but gives the travelled distance and the spent time in other unities. Let's first convert the unitys so we don't need to worry about the correctness of the answer later on:

`\begin{gathered} 1\text{ ft ---- 1.89}*10^(-4)\text{ miles} \\ 4777\text{ ft ---- x} \\ \\ x=\frac{\text{ 1.89}*10^(-4)*4777\text{ }}{1}=0.902\text{ miles} \end{gathered}`

Doing the same thing for the time spent:

`\begin{gathered} 1\text{ min --- 0.016 hrs} \\ 7.27\text{ min --- x } \\ \\ x=\frac{7.27*\text{0.016}}{1}=0.116\text{ hrs} \end{gathered}`

Step 2 - Finding the average speed

The average speed can be obtained by dividing the distance travelled by the time it took to travel. In mathematical notation:

`V=(d)/(\Delta t)`

We have already calculated that:

`\begin{gathered} d=0.902\text{ miles} \\ \\ \Delta t=0.116\text{ hrs} \end{gathered}`

Substituting these values on the equation, we get:

`V=(0.902)/(0.116)=7.77\text{ miles/hour}`

The velocity of the runner in miles per hour is thus 7.77 miles/hr. The closest alternative is 7.47 miles/hr.