Question

Joshua started walking from his home at noon and two hours later he reached the park, which is 3 mi away. his distance from home and the time he walks are related. write an equation that relates time and distance from home, assuming Joshua's speed is constant

Answer 1

He takes 2 hours to walk 3 miles.

If d is the distance and t is the time, and we are assuming a constant proportionality relationship between these two variables, we have:

`d=k\cdot t`

We can calculate k (in this case is the average speed) knowing that he takes 2 hours (t=2) to cover 3 miles (d=3). As this point (2,3) belongs to the line, we replace and calcualte:

`\begin{gathered} d=k\cdot t \\ 3=k\cdot2 \\ k=(3)/(2) \end{gathered}`

Then, we can write the relationship between distance d and time t as:

`d=(3)/(2)\cdot t`