Question

Two friends drive off in different directions from the same place. One heads North at 50 miles per hour, while the other heads East atr20 miles per hour. Complete an equation for the distance between the friends after t hours. Distance =

Answer 1

Each friend travelled for t hours

Recall, distance = speed x time

if one heads North at 50 miles per hour, then the distance that he covered after t hours is 50 x t = 50t

if the other heads East at 20 miles per hour, then the distance that he covered after t hours is 20 x t = 20t

The directions forms a right angle triangle as shown below

The distance after t hours is AC. We would find it by applying the pythagorean theorem which is expressed as

hypotenuse^2 = one leg^2 + other leg^2

hypotenuse = AC

one leg = 50t

another leg = 20t

`\begin{gathered} AC^2=\text{ }(50t)^2+(20t)^2 \\ AC^2=2500t^2+400t^2=2900t^2 \\ AC\text{ = }\sqrt[]{2900t^2} \\ AC\text{ = 53.85}t \end{gathered}`

The required equation is

Distance = 2500t^2 + 400t^2