Quadratic Functions, Equations and Inequalities - Applications of Quadratic Functions and Equations

At \(0800\text{ hrs}\), Bernard cycles from Town \(A\) to Town \(B\) which is \(100\text{ km}\) apart. Town \(M\) is half-way between Town \(A\) and Town \(B\). Bernard's average speed from Town \(A\) to Town \(M\) is \(x\text{ km/h}\). From Town \(M\) to Town \(B\), his average speed is increased by \(2\text{ km/h}\). The difference in time taken is \(20\) minutes.

1. Write down an expression for the time taken to travel
   1. from Town \(A\) to Town \(M\),[1]
   2. from Town \(M\) to Town \(B\).[1]
2. Using your answers in (a), form an equation and show that it can be simplified to \(x^2 + 2x - 300 = 0\).[2]
3. Solve the equation \(x^2 + 2x - 300 = 0\).[3]
4. Find the time that Bernard arrives at Town \(B\).[2]