MathDB
Men Walking in A.P.

Source:

June 8, 2009
quadraticsalgebraquadratic formula

Problem Statement

Two men set out at the same time to walk towards each other from M M and N N, 72 72 miles apart. The first man walks at the rate of 4 4 mph. The second man walks 2 2 miles the first hour, 212 2\frac {1}{2} miles the second hour, 3 3 miles the third hour, and so on in arithmetic progression. Then the men will meet: <spanclass=latexbold>(A)</span> in 7 hours<spanclass=latexbold>(B)</span> in 814 hours<spanclass=latexbold>(C)</span> nearer M than N<spanclass=latexbold>(D)</span> nearer N than M<spanclass=latexbold>(E)</span> midway between M and N <span class='latex-bold'>(A)</span>\ \text{in 7 hours} \qquad <span class='latex-bold'>(B)</span>\ \text{in }{8\frac {1}{4}}\text{ hours}\qquad <span class='latex-bold'>(C)</span>\ \text{nearer }{M}\text{ than }{N}\qquad \\ <span class='latex-bold'>(D)</span>\ \text{nearer }{N}\text{ than }{M}\qquad <span class='latex-bold'>(E)</span>\ \text{midway between }{M}\text{ and }{N}