Question

A motorcycle and a car leave an intersection at the same time. the motorcycle heads north at an average speed of 20 miles per​ hour, while the car heads east at an average speed of 48 miles per hour. find an expression for their distance apart in miles at the end of t hours.

Answer 1

First, determine the distance of the motorcycle and the car from the start point. The distance could be determined using
$\boxed{d=v \times t}$
d stands for distance, v stands for speed, t stands for time

The car
d = 48 × t
d = 48t

The motorcycle
d = 20 × t
d = 20t

At the end of t hours, the car is 48t miles (east) from the start point and the motorcycle is 20t miles (north) from the start point.

Second, determine the distance between 48t miles at east and 20t miles at north using pythagoras
distance = $\sqrt{(48t)^{2}+(20t)^{2}}$
distance = $\sqrt{2304t^{2}+400t^{2}}$
distance = $\sqrt{2704t^{2}}$
distance = 52t

The expression for their distance apart at the end of t hours is 52t