I have a situation with 3 cars: A, B, and C. Cars B and C start at the same spot, while car A is already 15km ahead:
The velocities of the cars are:
$V_A = 50km/h$
$V_B = 40km/h$
$V_C = 60km/h$
The question is: is it possible that car C can be located exactly between car B and car A? The final answer dictates that the situation is not possible, but the equation I made suggests that it is, so I assume I made a mistake somewhere, but I can't seem to find where.
Here is how I did it:
Assume $t$ is the number of hours it took for the requested situation to occur:
It is obvious now that car C is just an average of the distances traveled by car A & B. If a solution exists, the following equation must be true:
$$\frac{(50t + 15) + 40t}{2} = 60t$$
When we try to solve for $t$, we get that:
$$90t + 15 = 120t \rightarrow 30t = 15 \rightarrow t = 1/2 \text{ hours}$$
If a solution exists, then the situation must occur -- this contrasts the final answer. Where is my mistake?
You are correct. After $\frac 12$ hour, $A$ is at $40$ km, $B$ is at $20$ km, $C$ is at $30$ km and $C$ is indeed halfway in between.