2016 AMC 8 Problems/Problem 4

Problem

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?

$\textbf{(A) }6\qquad\textbf{(B) }10\qquad\textbf{(C) }15\qquad\textbf{(D) }18\qquad \textbf{(E) }30$

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.

~CHECKMATE2021

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 $\boxed{\textbf{B) 10}}$

Video Solution

https://youtu.be/I9neY-xoG90?si=tDSd8my8W8Mb7Lqp

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Video Solution (THINKING CREATIVELY!!!)

https://youtu.be/r92zdVMTamI

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Video Solution

https://youtu.be/gKjWxvyNSjk

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2016 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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All AJHSME/AMC 8 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.

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2016 AMC 8 Problems/Problem 4

Contents

Problem

Solution 1

Solution 2

Video Solution

Video Solution (THINKING CREATIVELY!!!)

Video Solution

See Also