The Problem Solving Competition

Overview

Periodically, new problems will appear.
Bring your solutions to Bradley 476 by the date listed.
A correct solution earns a prize.
The most correct solutions over the course of the year earns an invitation to represent Bradley at the US National Collegiate Mathematics Championships,
which will be held in California in August.
Good luck!

Bradley Representatives

Problems

13 Apr
23 Feb

How Much Salt

200 pounds of salt is dissolved in a vat of water so that there are 600 gallons of salt water to begin a salt water experiment. Next, salt water containing 1 pound of salt per gallon of water is continuously pumped into the vat at the rate of 5 gallons per minute. Fluid is pumped out of the tank also at the rate of 5 gallons per minute. Assuming a uniform mixture of water and salt at times through agitation, find the amount of salt in the tank after 5 hours.

Reversed Digits as Ages

Part 1. A woman is 74 and her daughter is 47 at an instant in time. Are there any other ages when this woman and daughter will have, or have had, exactly reversed digits for their ages at a given instant?

Part 2. In general describe the circumstances and conditions under which any two given people (not necessarily mother and daughter) can have ages whose digits are exactly reversed from each other. An example for the general case would be 29 and 92 as a pair. Note: For both parts of this problem assume ages less than 100. You may also assume that 00, 01, 02, ... are the digits of the ages 0, 1, 2, ...

Define the Cooling Function Recursively

A freshly brewed cup of coffee is 200 degrees. The room is 70 degrees. The coffee cools to 180 degrees in 5 minutes. Write the cooling function for this situation recursively.

Minimize the Travel Time

Under new codes, builders must minimize the travel time from a corner of the top floor of a building to the opposite corner on the ground floor.

Consider a multilevel rectangular building with a square base. If each level is 8 feet high from floor to floor, if the average walking speed is 5 feet per second, and if the average elevator speed is 20 feet per second, find the dimensions of the building that satisfies the codes subject to the following constraints and assumptions. The total floor space is to be 80,000 square feet. A person walking across any floor walks without backtracking in hallways that are perpendicular to each other. The average speeds are maintained. There is no time lost waiting on elevators.

This page is maintained by Michael Lang.