Question

Two cars are racing at a constant speed around a circular racetrack. Car $A$ requires $15$ seconds to travel once around the racetrack and car $B$ requires $25$ seconds to travel once around the racetrack. If car $A$ passes car $B$, how many seconds will elapse before car $A$ once again passes car $B$?

• A. $\frac{75}{2}$ or $37.5$
• B. $40$
• C. $38$
• D. $36$
• E. $34$

Answer 1

The correct option is A $\frac{75}{2}$ or $37.5$

Say they’re both right next to each other at time $x=0$. You need to figure out how many seconds will go by before car $A$ has gone exactly one track length farther than car $B$ (which is when $A$ will pass $B$ again).

Car $A$: 1 track length every $15$ seconds. In $x$ seconds, travels $\frac{1}{15}x$ of the track.
Car $B$: $1$ track length every $25$ seconds. In$x$ seconds, travels $\frac{1}{25}x$ of the track.

Now, we need to find how many seconds elapse until $A$ has traveled one track length farther than $B$. It can be written in equation as;

$\frac{1}{15}x=\frac{1}{25}x+1$

Solving for $x$, we get

$\frac{1}{15}x-\frac{1}{25}x=1$

$\frac{5x-3x}{75}=1$

$2x=75$

$x=\frac{75}{2}$

So, $37.5$ seconds will elapse before car $A$ once again passes car $B$.

Hence, option A is correct.