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1957 AMC 12 Question 39

AMC12 · 1957 AMC 12

Question 39

Two men set out at the same time to walk towards each other from $M$ and $N,$ $72$ miles apart. The first man walks at the rate of $4$ mph. The second man walks $2$ miles the first hour, $2\frac12$ miles the second hour, $3$ miles the third hour, and so on in arithmetic progression. Then the men will meet:
  1. in $7$ hours
  2. in $8\frac14$ hours
  3. nearer $M$ than $N$
  4. nearer $N$ than $M$
  5. midway between $M$ and $N$