Question

A Dodge Neon and a Mack truck leave an intersection at the same time. The Neon 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

d=50t

Explanation:

let S be speed, so

`S=(d)/(t)\\`

Then the distance would be:

`d=St`

`for the Neon:\\\\d_(N)=S_(N)t\\ \\for the Mack:\\\\d_(M)=S_(M)t`

Using the Pythagorean theorem :

`d=\sqrt{d_(N)^(2)+d_(M)^(2) }`

Replacing the given values:

`d=\sqrt{(30t)^(2)+(40t)^(2) }\\\\d=√(2500t^2)=50t`

where d is in miles and t in hours.