Q. In the middle of a vast prairie, a truck is stationed at the intersection of two perpendicular straight highways.

The truck travels at 50 miles per hour along the highways and at 14 miles per hour across the prairie.

Consider the set of points that can be reached by the firetruck within six minutes. The area of this region is m/n square miles, where m and n are relatively prime positive integers.

Find (m + n)?

• Let the roads be the x and y axes. The situation is symmetric across each of these, and also across y=x and y=-x, making a total of 8 parts. I will only consider the part between x axis and y=x.
  
  So, for distance x - z travelled at highway in
  
  x/50 - z/50 + sqrt(z^2 + y^2)/14 hrs.
  
  x/50 is constant for any x... so by differentiating and equating to 0, we gets
  
  z = 7y/24.
  
  So now we have the most optimal way to reach (x,y) from the origin: travel along the highway until (x-7y/24 , 0) and then travel along the prairie the rest of the way.
  
  Now we substitute and have:
  
  time=> 1/10 = (x/50)+(12y/1
• 15 years agoHelpfull: Yes(2) No(0)
• 700+31=731
• 15 years agoHelpfull: Yes(0) No(0)
• 731
• 15 years agoHelpfull: Yes(0) No(0)
• 700+31=731
• 10 years agoHelpfull: Yes(0) No(0)