Travel Time Problem Leading to a Quadratic Equation

A trailer travels its entire \(80\) km journey at an average speed of \(x\) km/h.

1. Write down, in terms of \(x\), for the time taken, in hours, for the trailer to travel its journey.

On a certain day, due to heavy traffic, the trailer was delayed and took \(30\) minutes longer than scheduled to travel the first \(20\) km.

The remainder of the journey was completed at an average speed of \(\left( x+20 \right)\)km/h.

2. Write down an expression, in terms of \(x\), for the time taken, in hours, to travel
   1. the first \(20\) km,
   2. the remaining journey.
3. On the day of the delay, the trailer managed to arrive at its destination on time.
   1. Write down an equation in \(x\), and show that it reduces to \({{x}^{2}}+20x-2400=0\).
   2. Solve \({{x}^{2}}+20x-2400=0\).
4. Find the time taken for the normal scheduled journey.