Speedway Trials

What do the names Duesenberg, Stutz and Bugatti have in common ?
To qualify for the big race , Enzo needs to average 60 miles/hour overall in his two warm-up heats, each heat one mile long. In the first heat he could only muster a 30 mile per hour average. How fast must Enzo drive in his second heat to qualify for the final ? Will he be able to qualify ?

Originally posted by HS Thomas:
What do the names Duesenberg, Stutz and Bugatti have in common ?

1. They are all words.
2. None of them is 42 letters long.
3. All three have repeated letters.
4. All contain a "U".
5. Saying them rapidly and in the right sequence will open the secret realm of Narnia.
6. None would make a good name for a little girl.

To qualify for the big race , Enzo needs to average 60 miles/hour overall in his two warm-up heats, each heat one mile long. In the first heat he could only muster a 30 mile per hour average. How fast must Enzo drive in his second heat to qualify for the final ? Will he be able to qualify ?

Enzo can't qualify. Why?
To average 60 mph over the two miles, he must cover the two miles in a total of two minutes or less (h1 and h2 are the heat times in minutes):
2 miles / 2 Minutes * 60 Minutes/Hour = 60 mph
h1 + h2 <= 2 Minutes
It takes two minutes to drive one mile at 30mph, which Enzo did in heat 1:
h1 = (1 Mile / 30 Miles/Hour * 60 Minutes/Hour) = 2 Minutes
Substitute the values:
2 Minutes + h2 <= 2 Minutes
The only satisfactory values for h2 are 0 or less. Enzo can't qualify.

He has to average 90 mph in the next heat. But it sounds impossible.

Originally posted by HS Thomas:
What do the names Duesenberg, Stutz and Bugatti have in common ?

These are names of three people who have never been in my kitchen.

These are names of three people who have never been in my kitchen
Thank you, Clavin.

Shal: Enzo has already taken two minutes to travel one mile at 30 mph. If he travels the second mile at 90 mph, that will take 40 seconds. So, in two minutes and 40 seconds, he has traveled two miles. What's his average speed then?

Here is a program that shows the relationship between the speed of heat one (X-Axis) and heat two (Y-Axis). The value of heat 2 actually is "Infinity" at 30 mph. You can see that the resulting curve approaches a limit of 30 MPH on both X and Y axes, but never reaches 30 MPH.
I copied almost all of this code from a recent posting by Jim Yingst-- I hope that's okay.

import java.awt.*;
import javax.swing.*;
// Almost all of this code is from a program by
// Jim Yingt
public class Enzo extends JFrame {
  public Enzo() {
    super("Can Enzo Qualify?");
    setContentPane(new GraphPanel());
    setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    pack();
    Dimension screen = Toolkit.getDefaultToolkit().getScreenSize();
    this.setLocation(
      (screen.width - getWidth()) / 2,
      (screen.height - getHeight()) / 2);
    setVisible(true);
  }
  public static void main(String[] args) {
    new Enzo();
  }
  private static class GraphPanel extends JPanel {
    public GraphPanel() {
      setBackground(Color.white);
      setForeground(Color.black);
      setPreferredSize(new Dimension(400, 400));
    }
    public void paintComponent(Graphics g) {
      super.paintComponent(g);
      // paint the axes
      g.setColor(Color.black);
      g.drawString("heat 1 mph", 200, 390);
      for (int x = 0; x < 400; x += 30) {
        g.drawString(new Integer(x).toString(), x, 380);
      }
      for (int y = 0; y < 400; y += 50) {
        g.drawString(new Integer(y).toString(), 20, 400 - y);
      }
      double oldH1 = 0;
      double oldH2 = 400;
      g.setColor(Color.red);
      for (double heat1 = 1; heat1 < 400; heat1 += .1) {
        double heat2 = howFastIsHeat2(heat1);
        if (heat2 > 0) {
          if (oldH1 > 0 && oldH2 > 0) {
            g.drawLine((int)heat1, 400 - (int)heat2, (int)oldH1, 400 - (int)oldH2);
          } else {
            g.drawLine((int)heat1, 400 - (int)heat2, (int)heat1, 400 - (int)heat2);
          }
        }
        oldH1 = heat1;
        oldH2 = heat2;
      }
    }
    private double howFastIsHeat2(double mphH1) {
      // mphH1 comes in miles per hour
      double minutesH1 = 60 / mphH1;
      double minutesH2 = 2 - minutesH1;
      double mphH2 = 1 / minutesH2 * 60;
      return mphH2;
    }
  }
}

What do the names Duesenberg, Stutz and Bugatti have in common ?
They're all old sports cars (the first I learned from reading too many Clive Cussler novels, the last from my husband's car magazines... so I figured the 2nd was one too)
Dusenberg, Stutz and Bugatti