2016 AMC 8

Complete problem set with solutions and individual problem pages

Problem 4 Easy

When Cheenu was a boy, he could run 15 miles in 3 hours and 30 minutes. As an old man, he can now walk 10 miles in 4 hours. How many minutes longer does it take for him to walk a mile now compared to when he was a boy?

  • A.

    6

  • B.

    10

  • C.

    15

  • D.

    18

  • E.

    30

Answer:B

Solution 1

When Cheenu was a boy, he could run 15 miles in 3 hours and 30 minutes = 3\times60 + 30 minutes = 210 minutes, thus running \frac{210}{15} = 14 minutes per mile. Now that he is an old man, he can walk 10 miles in 4 hours = 4 \times 60 minutes = 240 minutes, thus walking \frac{240}{10} = 24 minutes per mile. Therefore, it takes him \boxed{\textbf{(B)}\ 10} minutes longer to walk a mile now compared to when he was a boy.

 

Solution 2

From the question, the old man can travel five miles in two hours, so we can set both speeds to 15 miles. We can see that Cheenu as an old man takes 2 hours and 30 minutes for him to travel 15 miles, which is also 150 minutes. We can then divide this by fifteen, which gives us 10, thus the answer is \boxed{\textbf{B) 10}}