Q. 109 - Precalculus Enhanced with Graphing Utilities

Question

Distance between Moving Objects A Ford Focus and a Mack truck leave an intersection at the same time. The Focus heads east at an average speed of 30 miles per hour,

while the truck heads south at an average speed of 40 miles per hour. Find an expression for their distance apart d (in miles) at the end of t hours.

Step-by-Step Solution

Answer

The expression for their distance apart d (in miles) at the end of t hours is $d=50t$

Step 1. Given Information

The Focus heads east at an average speed of 30 miles per hour, while the truck heads south at an average speed of 40 miles per hour.

Step 2. Finding equation

Since one is heading east and another to south. The distance is the hypotenuse of right triangle and sides of the legs are found by multiplying $t$ by the car's speed.

$$\begin{gathered} d^2={\left(30t\right)}^2+{\left(40t\right)}^2 \\ {d}^2=900t^2+1600t^2 \\ {d}^2=2500t^2 \\ d=50t \end{gathered}$$