# Speedway Trials

HS Thomas

Ranch Hand

Posts: 3404

posted 12 years ago

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 ?

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

posted 12 years ago

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.

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.

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

Jim Yingst

Wanderer

Sheriff

Sheriff

Posts: 18671

posted 12 years ago

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?

**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?

"I'm not back." - Bill Harding, *Twister*

Timothy Chen Allen

Ranch Hand

Posts: 161

posted 12 years ago

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.

I copied almost all of this code from a recent posting by Jim Yingst-- I hope that's okay.