Question

Two​ vehicles, a car and a​ truck, leave an intersection at the same time. the car heads east at an average speed of 50 miles per​ hour, while the truck heads south at an average speed of 60 miles per hour. find an expression for their distance apart d​ (in miles) at the end of t hours.

Answer 1

The car heads east at an average speed of 50 miles per​ hour from the intersection point towards East. The truck heads east at an average speed of 60 miles per​ hour from the intersection point towards South.

The distance of car from the intersection point after t hours is $50t$.

The distance of truck from the intersection point after t hours is $60t$.

Since these distances are perpendicular to each other, distance apart d​ (in miles) at the end of t hours is

$d=\sqrt{(50t)^2+(60t)^2} \\ d=10\sqrt{61} t\\ d=78.1t$

Thus the distance apart is $d=78.1t \;miles$