Question

Two cars are moving in the same direction at the same speed u. The cars maintained a constant distance x between them. An another car (third car) coming from opposite direction meets the two cars at an interval of t. Then find the speed of the third car.

• A. $\frac{x}{t}tu$
• B. $\frac{x}{t}$
• C. $u - \frac{x}{t}$
• D. $\frac{x}{t} - u$

Answer 1

Answer: (D)

$\frac{x}{t} - u$

Answer 2

Let the speed of the two cars be $u$ and the distance between them be $x$. Let the speed of the third car be $v$. The third car meets the two cars at an interval of $t$. When the third car meets the first car, the second car is at a distance $x$ from the meeting point. The relative speed between the third car (moving with speed $v$ in one direction) and the second car (moving with speed $u$ in the opposite direction relative to the third car's initial direction of travel from the meeting point) is $v+u$. This relative speed covers the distance $x$ in time $t$. Therefore, $x = (v+u)t$. Solving for $v$, we get $v = \frac{x}{t} - u$.