AMC 10 Weekly Practice Round 2

Complete problem set with solutions and individual problem pages

Problem 18 Easy

Andy was training on a circular track 400 meters long. After completing the first lap, he felt that his performance was not ideal. So he increased his speed by 15\%, and as a result, he finished the lap 9 seconds faster than in the first lap. How many seconds did it take him to run the first lap?

  • A.

    68

  • B.

    69

  • C.

    70

  • D.

    71

  • E.

    72

Answer:B

Let t be the time Andy took to run the first lap.

From the problem, Andy’s speed for the first lap is: \text{distance} \div \text{time} = 400 \div t = \frac{400}{t}.

Increasing his speed by 15\% for the second lap, the speed becomes: (1 + 15\%) \times \frac{400}{t} = \frac{460}{t}.

Thus, the time taken for the second lap is: \text{distance} \div \text{speed} = 400 \div \left( \frac{460}{t} \right) = \frac{20t}{23}.

Since the second lap is 9 seconds faster than the first lap: t - \frac{20t}{23} = 9,

which gives t = 69 seconds.

Therefore, Andy took 69 seconds to run the first lap.

Related Problems
Problem 16 AMC 10 Weekly Practice Round 2
Problem 17 AMC 10 Weekly Practice Round 2
Problem 19 AMC 10 Weekly Practice Round 2
Problem 20 AMC 10 Weekly Practice Round 2
Think Academy Powered by ChatGPT