Alberto, Bernardo, and Carlos competed in a race, during which each of them ran at a constant speed throughout the course. When Alberto crossed the finish line, Bernardo and Carlos were 36 and 46 meters behind him, respectively. When Bernardo crossed the finish line, Carlos was 16 meters behind him. What is the length of the track?
A) $96 \mathrm{~m}$
B) $100 \mathrm{~m}$
C) $120 \mathrm{~m}$
D) $136 \mathrm{~m}$
E) $144 \mathrm{~m}$
Solution

## ALTERNATIVE A

Let $x$ be the length in meters of the track. The distance between Bernardo and Carlos was 10 meters when Alberto crossed the finish line, and it was 16 meters when Bernardo crossed the finish line. Thus, during the time interval in which Alberto and Bernardo completed the race, Bernardo ran 36 meters while Carlos ran 30 meters; hence,

$$
\frac{\text { speed of Carlos }}{\text { speed of Bernardo }}=\frac{30}{36}=\frac{5}{6}
$$

Since Bernardo crossed the finish line 16 meters ahead of Carlos, we have the equation $\frac{5}{6}=\frac{x-16}{x}$, whose solution is $x=96$.