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# Speedway Trials

HS Thomas
Ranch Hand
Posts: 3404
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 ?

Timothy Chen Allen
Ranch Hand
Posts: 161
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.

Shalu Ban
Ranch Hand
Posts: 72
He has to average 90 mph in the next heat. But it sounds impossible.

fred rosenberger
lowercase baba
Bartender
Posts: 12234
36
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.

Jim Yingst
Wanderer
Sheriff
Posts: 18671
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?

Timothy Chen Allen
Ranch Hand
Posts: 161
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.

Jessica Sant
Sheriff
Posts: 4313
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