1955 AHSME Problems/Problem 10

How many hours does it take a train traveling at an average rate of 40 mph between stops to travel a miles it makes n stops of m minutes each?

$\textbf{(A)}\ \frac{3a+2mn}{120}\qquad\textbf{(B)}\ 3a+2mn\qquad\textbf{(C)}\ \frac{3a+2mn}{12}\qquad\textbf{(D)}\ \frac{a+mn}{40}\qquad\textbf{(E)}\ \frac{a+40mn}{40}$

Solution

The train will take $\frac{a}{40}$ hours to travel $a$ miles, and it takes $\frac{nm}{60}$ . The LCM of $40$ and $60$ is $120$ , which allows for the addition of the fractions $\frac{3a}{120}$ and $\frac{2mn}{120}$ . The end result is $\boxed{\textbf{(A)}\frac{3a+2mn}{120}}$ .

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1955 AHSME Problems/Problem 10

Solution

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