A fishing boat, the Clairbuoyant, sails 40 miles east, then 80 miles south, and finally 20 miles east again. How far is it from its starting point?

## Set 01

## Distance

You and a friend are each flying your own small jet airplane. You both take off from Cleveland Hopkins Airport at 12:00 noon. You are traveling due east and your friend is traveling due south. You are traveling at *x* miles per hour and your friend is traveling at *y* miles per hour. Use the Pythagorean Theorem to make up a formula for how far apart your two planes are after *t* hours of flying.

## Radio Antenna

A piece of wire for a radio antenna is to be strung from the roof of Andrea’s house to the roof of the garage. The garage is 40 feet from the house. The roof of the house is 45 feet high at the edge where the wire is fastened, and the roof of the garage is 15 feet high. The wire must be at least how long?

## Defined Operations 1

Define an operation $ for positive real numbers so that *a* $ *b = ab*/(*a* + *b*).

Then 4 $ (4 $ 4) = what?

## Triangle, Sides, and Perimeter

The lengths of the sides of a triangle measured in inches are three consecutive integers. The length of the shortest side is 30% of the perimeter. Find the lengths of the three sides.

## Pet Rocks

The town of Ware has exactly 5000 families. Every family has 0, 1, or 2 pet rocks. Every pet rock belongs to a family. Most families have 1 pet rock. Exactly half of the remaining families have 2 pet rocks. How many pet rocks are there in Ware?

## Doctors and Lawyers

The average (arithmetic mean) age of a group of doctors and lawyers is 40. If the doctors average 35 years of age and the lawyers average 50 years of age, then the ratio of the number of doctors to the number of lawyers is:

- 3:2
- 3:1
- 2:3
- 2:1
- 1:2

## Foul Shots

Igor, on the varsity basketball team, has made 36 of his 80 foul shots so far this season. What is his percent accuracy? How many foul shots must he make in a row to bring his average up to 50%?

## Giant Difference of Squares

Find the sum of the squares of all real numbers, *x*, satisfying the equation

x^{256}– 256^{32}= 0.

- 8
- 128
- 512
- 65,536
- 2(256
^{32})

## Inequality

If *r* > 0, then for all *p* and *q* such that *pq* does not equal 0 and such that *pr* > *qr*, we have:

- –
*p*> –*q* - –
*p*>*q* - 1 >
*q*/*p* - 1 <
*q*/*p* - none of these