3 A marathon has 8.000 , unners \( 70 \% \) domplete the race, Of those who finish \( 4 / 5 \) tomplete it in under 4 hours. Of the remaining finishers. \( 25 \% \) complete it in the last hou before the time limit. - (a) What percentage of all runners complete the race in under 4 hours? (b) What percentage of all runners fmish in the last hour before the time limit?
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Let’s break it down! First, we know 70% of the 8,000 runners complete the marathon. So, \( 0.70 \times 8000 = 5600 \) finishers. Of these, \( \frac{4}{5} \) finish in under 4 hours. That’s \( \frac{4}{5} \times 5600 = 4480 \) finishers completing under 4 hours. To find the percentage of all runners, we take \( \frac{4480}{8000} \times 100 = 56\% \). Next, we’re told that of the remaining finishers (those not completing under 4 hours), 25% finish in the last hour before the time limit. First, find remaining finishers: \( 5600 - 4480 = 1120 \). Then, \( 0.25 \times 1120 = 280 \) finishers complete in the last hour. To find the percentage of all runners, we have \( \frac{280}{8000} \times 100 = 3.5\% \). So, - (a) 56% complete the race in under 4 hours. - (b) 3.5% finish in the last hour before the time limit.
