Two guns were fired from the same place at an interval of $11 \text{ minutes}$. A person in a train approaching the place hears the second shot $10 \text{ minutes}$ after hearing the first. If the speed of sound is $330 \text{ m/s}$, find the speed of the train.

Options:

• A: $33 \text{ m/s}$
• B: $30 \text{ m/s}$
• C: $36 \text{ m/s}$
• D: $40 \text{ m/s}$

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?