A stopwatch starts when a train enters a tunnel and stops when the entire train has completely exited it.
A $362$ meter freight train took $85$ seconds to do this.
A $254$ meter bullet train that travels two times faster than the freight train does this in $38$ seconds.
a) Find the length of the tunnel in meters.
b) Find the speed of the freight train in meters/second.

Find values for $x$ and $y$ that satisfy the following equation.
$$2x+9y+15=x-y=4x+2y-9$$

Solve the following simultaneous equation.
$$\begin{cases} \frac{3}{x+y}+\frac{2}{x-y}=-1 \\ \frac{9}{x+y}-\frac{5}{x-y}=-14 \end{cases}$$

Fill in the blank with a number.
$$\begin{align}
a+b+c & = 56 \\
a^2+b^2+c^2 & = 1344 \\
a^2 & = bc \\
abc & = \fbox{$\phantom{xx}$} \\
\end{align}$$

You have $250$ ml of salt solution $A$ and $150$ ml of salt solution $B$. If you mix solution $A$ and $B$, the mixed solution contains $10.2\%$ salt. Also, if you take $100$ ml from solution $A$ and replace it with $100$ ml of water, the new concentration is equal to $B$’s concentration. Find the original concentrations of salt solution $A$ and $B$. Include the $\%$ sign in your answers.

Rearrange and simplify $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$ to make $u$ the subject. Your answer should be a single fraction.

$a,b$ and $c$ are positive integers such that the simultaneous equations $(a-2b)x=1$,$(b-2c)x=1$ and $x+25=c$ have a positive solution for $x$. What is the minimum value of $a$?