Question

Two​ vehicles, a car and a​ truck, leave an intersection at the same time. The car 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.

Answer 1

Explanation:

the car distance to the intersection will be

30t (30 miles for every hour).

the truck distance to the intersection will be

40t (40 miles for every hour).

the distance between the car and the truck will always be the Hypotenuse of a right-angled triangle with the legs being the actual distances from the starting intersection.

so, we use Pythagoras :

d² = (30t)² + (40t)² = 900t² + 1600t² = 2500t²

d = sqrt(2500t²) = 50t

so, their distance will increase 50 miles every hour.