2018 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 2 Easy

Sam drove 96 miles in 90 minutes. His average speed during the first 30 minutes was 60 mph (miles per hour), and his average speed during the second 30 minutes was 65 mph. What was his average speed, in mph, during the last 30 minutes? (2018 AMC 10B Problem, Question#1)

  • A.

    64

  • B.

    65

  • C.

    66

  • D.

    67

  • E.

    68

Answer:D

Let Sam drive at exactly 60 mph in the first half hour, 65 mph in the second half hour, and x mph in the third half hour.

Due to rt=d, and that 30 min is half an hour, he covered  60 \cdot \frac{1}{2}=30 miles in the first 30 mins.

Similarly, he covered \frac{65}{2} miles in the 2\rm nd half hour period.

The problem states that Sam drove 96 miles in 90 min, so that means that he must have covered 96-\left(30+ \frac{65}{2}\right)=33 \frac{1}{2} miles in the third half hour period.

rt=d, so x \cdot \frac{1}{2}=33 \frac{1}{2}.

Therefore,Sam was driving (\rm D) \ 67 miles per hour in the third half hour.

Related Problems
Problem 1 2018 AMC 10 B
Problem 3 2018 AMC 10 B
Problem 4 2018 AMC 10 B
Problem 5 2018 AMC 10 B
Think Academy Powered by ChatGPT