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.

Respuesta :

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 [tex] 50t [/tex].

The distance of truck from the intersection point after t hours is [tex] 60t [/tex].

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

[tex] d=\sqrt{(50t)^2+(60t)^2} \\
d=10\sqrt{61} t\\
d=78.1t [/tex]

Thus the distance apart is [tex] d=78.1t \;miles [/tex]