AMC 8 Daily Practice Round 11

Complete problem set with solutions and individual problem pages

Problem 25 Easy

A plane can fly for a maximum of 8.5 hours in the air. On its journey, the plane travels at an average speed of 900 \, \text{km/h} going to its destination and 800 \, \text{km/h} on the return trip. What is the greatest distance (in kilometers) the plane can travel one way before it must turn back to ensure it does not exceed its flight time?

  • A.

    3825\text{km}

  • B.

    3400\text{km}

  • C.

    3500

  • D.

    3600\text{km}

  • E.

    3612.5\text{km}

Answer:D

Let the maximum one-way distance the plane can travel be x kilometers. Based on the problem, the equation is

\frac{x}{900} + \frac{x}{800} = 8.5.

Simplifying, we find

8x + 9x = 61200 \quad \Rightarrow \quad 17x = 61200 \quad \Rightarrow \quad x = 3600.

After verification, x = 3600 satisfies the original equation. Therefore, the plane can travel a maximum of 3600 \, \text{km} one way.

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Problem 24 AMC 8 Daily Practice Round 11
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