Two towns A and B are $100 \text{ km}$ apart. A car starts from A towards B at $15 \text{ km/h}$ and another car starts from B towards A at exactly the same time at $25 \text{ km/h}$. After how much time will they meet?

Options:

• A: $2 \text{ hours}$
• B: $2.5 \text{ hours}$
• C: $3 \text{ hours}$
• D: $3.5 \text{ hours}$

Related Practice Questions:

• Let $S_1$ and $S_2$ be two disjoint, non-empty convex sets in $\mathbb{R}^n$. Under which of the following conditions is there guaranteed to exist a hyperplane that strictly separates $S_1$ and $S_2$?
• Let the primal linear programming problem be: Maximize $Z = c^T x$ subject to $Ax \le b, x \ge 0$. If this primal problem has an unbounded optimal objective value, then which of the following statements is always true regarding its dual problem?
• Let $S = \{(x, y) \in \mathbb{R}^2 \mid x^2 + y^2 \le 9\}$ be a convex set in $\mathbb{R}^2$. The set of all extreme points of $S$ is given by:
• In a linear programming problem with $3$ independent equality constraints and $5$ variables (including slack/surplus variables), what is the maximum possible number of basic solutions?