Maths Olympiad Prep

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Algebra Difficulty 6.9 National olympiad Find the answer

Steve plants ten trees every three minutes. If he continues planting at the same rate, how long will it
take him to plant 2500 trees?

(A) 1 1/4\textbf{(A)}\ 1~1/4(B) 3\textbf{(B)}\ 3(C) 5\textbf{(C)}\ 5(D) 10\textbf{(D)}\ 10(E) 12 1/2\textbf{(E)}\ 12~1/2

Multiple choice: answer with the letter of the option you want.

Solution

1. First, determine the rate at which Steve plants trees. He plants 10 trees every 3 minutes.
2. Calculate the number of trees Steve plants in one minute:
Trees per minute=10 trees3 minutes=103 trees per minute \text{Trees per minute} = \frac{10 \text{ trees}}{3 \text{ minutes}} = \frac{10}{3} \text{ trees per minute}
3. Next, calculate the number of trees Steve plants in one hour (60 minutes):
Trees per hour=(103 trees per minute)×60 minutes=10×603=200 trees per hour \text{Trees per hour} = \left(\frac{10}{3} \text{ trees per minute}\right) \times 60 \text{ minutes} = \frac{10 \times 60}{3} = 200 \text{ trees per hour}
4. Now, determine how many hours it will take Steve to plant 2500 trees:
Time in hours=2500 trees200 trees per hour=12.5 hours \text{Time in hours} = \frac{2500 \text{ trees}}{200 \text{ trees per hour}} = 12.5 \text{ hours}
5. Convert 12.5 hours to a mixed number:
12.5 hours=1212 hours 12.5 \text{ hours} = 12 \frac{1}{2} \text{ hours}

Thus, it will take Steve 12.5 hours to plant 2500 trees.

The final answer is 1212\boxed{12 \frac{1}{2}}

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.