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A spreading rumour

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The number of people who have heard a rumour doubles every $15$ minutes. At noon $2400$ people have heard it. How many minutes before noon had exactly $300$ people heard it?

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Hint

Halve backwards from noon until you reach the smaller count.

Solution

Going back $15$ minutes halves the count: $\frac{2400}{2} = 1200$ .
Halving again gives $\frac{1200}{2} = 600$ , and once more gives $\frac{600}{2} = 300$ .
That is $3$ halvings, so the time is $3 \times 15 = 45$ minutes before noon, and the answer is $45$ .

Answer: $45$

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