1. A competition problem requires one hour to fully develop (write, proofread, edit, and typeset). This problem is then given to 30,000 students, each working an average of 24 seconds to solve the problem. What is the ratio of a problem's development time to the total time spent by the students to solve the problem? Express your answer as a common fraction.

2. Select any three-digit multiple of 3. Calculate the sum of the cubes of the digits of that number. This is now your new number. Now calculate the sum of the cubes of the digits of this new number. Continue this procedure of adding the cubes of the digits of the resulting number until you arrive at a number that is equal to the sum of the cubes of its digits. What is this number?

3. Emma and Ed walk into a room containing 30 assembled Tworks and enough pieces to assemble 100 more Tworks. A Twork takes eight minutes to assemble and 10 minutes to disassemble. If Emma starts assembling Tworks as Ed begins disassembling the ones that were already made, and they both continue to work until there are exactly 35 assembled Tworks in the room (and no partially assembled or disassembled Tworks), how many minutes will Emma have worked?