# Thread: Distance Between Moving Objects

1. ## Distance Between Moving Objects

A Dodge Neon and a Mack truck leave an intersection at the same time. The Neon heads east at an average speed of 30 mph, while the truck heads south at an average speed of 40 mph. Find an expression for their distance apart d (in miles) at the end of t hours.

At first sight, I quickly decided to set up my table for D = rt. I also know that moving vehicles starting at the same location and traveling in opposite directions have equal distances if a TOTAL DISTANCE is given, which is clearly not the case here. However, this led nowhere. The question is asking for an expression for their distance apart denoted by d in miles. Seeking one or two hints.

2. ## Re: Distance Between Moving Objects

The distance between the two vehicles is the distance the truck has traveled minus the distance the neon has traveled.

3. ## Re: Distance Between Moving Objects

Think of a right triangle....OK?

4. ## Re: Distance Between Moving Objects

Originally Posted by HallsofIvy
The distance between the two vehicles is the distance the truck has traveled minus the distance the neon has traveled.
Ouch! I completely missed that the vehicles are going in different directions! Yes, with one vehicle moving east at 30 mph and the other south at 40 mph, after t hours the straight line between them is the hypotenuse of a right triangle with leg lengths 30t and 40t.

5. ## Re: Distance Between Moving Objects

It's a right triangle.
The hypotenuse = 50 mph
d = 50t, t in hours, d in miles.

Where did 50 mph come from?

6. ## Re: Distance Between Moving Objects

Originally Posted by harpazo

It's a right triangle.
The hypotenuse = 50 mph
d = 50t, t in hours, d in miles.

Where did 50 mph come from?
If we orient our coordinate axes such that the intersection is at the origin, and units are miles, with time t in hours, then the position of the Neon at time t is:

$\displaystyle (30t, 0)$

And the position of the Mack is:

$\displaystyle (0,-40t)$

Thus, the distance $\displaystyle d$ between them is:

$\displaystyle d(t)=\sqrt{(30t-0)^2+(0+40t)^2}=50t$

7. ## Re: Distance Between Moving Objects

...or a growing 3-4-5 right triangle

8. ## Re: Distance Between Moving Objects

Originally Posted by MarkFL
If we orient our coordinate axes such that the intersection is at the origin, and units are miles, with time t in hours, then the position of the Neon at time t is:

$\displaystyle (30t, 0)$

And the position of the Mack is:

$\displaystyle (0,-40t)$

Thus, the distance $\displaystyle d$ between them is:

$\displaystyle d(t)=\sqrt{(30t-0)^2+(0+40t)^2}=50t$
You are simply amazing! I love the way you reason your way to the answer.