What is the Speed of the Truck?

Date: 20 Mar 1995 20:28:17 -0500
From: Anonymous
Subject: A hard math problem

Dear Dr. Math, 

I have a math problem for you.  See if you can solve it.

1.  A storm is 50 miles offshore and its path is perpendicular 
     to a straight shoreline.  It is approaching the shore at a rate 
     of 4mph.  A van traveling along the shore wants to stay exactly 
     50 miles from the storm and remain on the shoreline.  The van 
     starts at the point on the shoreline in the path of the storm.

        a. Determine a formula for the speed that the truck 
            must maintain to remain 50 miles from the storm.

        b. Find the speed of the truck when the storm is 
            40 miles from the shore.

Please reply if you can.  Thanks so much.

                                              Sincerely,

                                              Chad Martin

Date: 21 Mar 1995 21:50:01 -0500
From: Dr. Ken
Subject: Re: A hard math problem

Hello there!

Here's how I would tackle this problem.  Label the van 
by the letter, V, the van's starting point by the letter, 
B, and the storm by the letter, S.  Then we know that 
the triangle VBS is a right triangle.  Now label the sides
opposite V, B, and S by the small letters v, b, and s.  
Then we know that b=50, and so v^2 + s^2 = 2500.  

Now find an equation for the distance the storm is away 
from the shore (in terms of time), and plug that into the 
above formula, substituting for v.  Then you should be 
able to solve for v.  

That will give you the DISTANCE the van has to go as a 
function of time.  Do you know how to find the velocity 
function when you have the distance function (think 
Calculus)?

Hope this helps.  Write back if you're still confused.

-Ken "Dr." Math