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Weekly Problem 44 - 2008

Stage: 3 Short Challenge Level: Challenge Level:1

Rudolf takes one hour to set $30$ questions, so he takes $2$ minutes to set each question. We're told each person takes half as long as the previous person to set questions, so we can work out how long each person takes to set one question, then multiply by the number of questions to give the time each setter spent on all their questions:

Setter
Time taken to set each question (minutes)
Number of questions set Total time spent setting questions (minutes)
John $8$ $25$ $200$
Peter $4$ $26$ $104$
Rudolf $2$ $30$ $60$
Susie $1$ $39$ $39$
Tony $\frac{1}{2}$ $55$ $27 \frac{1}{2}$

So in total the setters spent: $$ 200+104+69+39+27 \frac{1}{2} \;\text{minutes}= 430 \frac{1}{2} \text{minutes} $$ or $$7 \; \text{hours } \; 10 \; \text{minutes }\; 30 \; \text{seconds }$$ setting questions.

This problem is taken from the UKMT Mathematical Challenges.

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