Imran drives a distance of 180 km on a business trip. He drives the first 100 km at an average speed of x km/h. He drives at an average speed 5 km/h slower than this for the remainder of the journey.

1. (a)Find, in terms of x, an expression for the time taken, in hours, for the first 100 km.[1]
2. (b)Given that the journey takes a total of 2 hours 30 minutes, form an equation in x and show that it simplifies to x²-77x + 200 = 0.[4]
3. (c)Solve the equation x²-77x + 200 = 0, giving each answer correct to 2 decimal places.[4]
4. (d)Which of the solutions in part (c) represents the speed for the first 100 km of Imran's trip? Give a reason for rejecting the other solution.[1]
5. (e)Find the difference between the times taken for the first and second parts of the journey. Give your answer in minutes, correct to the nearest minute.[2]