6211
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2011-02-01T00:00:01
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<mdoxml version="1.0"><p>John, Peter, Rudolf, Susie and Tony decide to set some questions for the Schools Mathematical Challenge.</p>
<p> </p>
<p>John thinks up twenty-five questions and circulates them to the others. Peter, not wishing to be outdone, then sends twenty-six questions. Rudolf decides he had better get cracking and produces thirty questions. Susie sets to and comes up with thirty-nine posers, only to be beaten by Tony who produces fifty five stunning problems.</p>
<p> </p>
<p>If each person takes half as long as the previous person to set each question, and Rudolf takes one hour to set all his questions, then what is the total time spent settting questions?</p>
<p> </p>
<p>If you liked this problem, <a href="http://nrich.maths.org/6424">here is an NRICH task</a> which challenges you to use similar mathematical ideas.</p>
<p> </p>
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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:<br></br>
<br></br>
<table border="1">
<tbody>
<tr>
<td style="font-weight: bold; text-align: center;">Setter</td>
<td>
<div style="text-align: center; font-weight: bold;">Time taken to
set each question (minutes)</div>
</td>
<td style="text-align: center; font-weight: bold;">Number of
questions set</td>
<td style="text-align: center; font-weight: bold;">Total time spent
setting questions (minutes)</td>
</tr>
<tr>
<td style="text-align: center;">John</td>
<td style="text-align: center;">$8$</td>
<td style="text-align: center;">$25$</td>
<td style="text-align: center;">$200$</td>
</tr>
<tr>
<td style="text-align: center;">Peter</td>
<td style="text-align: center;">$4$</td>
<td style="text-align: center;">$26$</td>
<td style="text-align: center;">$104$</td>
</tr>
<tr>
<td style="text-align: center;">Rudolf</td>
<td style="text-align: center;">$2$</td>
<td style="text-align: center;">$30$</td>
<td style="text-align: center;">$60$</td>
</tr>
<tr>
<td style="text-align: center;">Susie</td>
<td style="text-align: center;">$1$</td>
<td style="text-align: center;">$39$</td>
<td style="text-align: center;">$39$</td>
</tr>
<tr>
<td style="text-align: center;">Tony</td>
<td style="text-align: center;">$\frac{1}{2}$</td>
<td style="text-align: center;">$55$</td>
<td style="text-align: center;">$27 \frac{1}{2}$</td>
</tr>
</tbody>
</table>
<br></br>
<div>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.</div>
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Weekly Problem 44 - 2008
John, Peter, Rudolf, Susie and Tony decide to set some questions for the Schools Mathematical Challenge. Can you work out how long in total they spend setting questions?
Measures and Mensuration
Time