Speed

A car departs from City A to City B via a highway. If the car travels at an average speed of \(60\) km/h, it will take \(x\) hours to arrive in City B; If the car travels at an average speed of \(90\) km/h, it will take \(3\frac{1}{3}\) hours to arrive in City B.

1. Find the value of \(x\). Hence state the distance between City A and City B via the highway.
2. If the car travels at an average speed of \(60\) km/h for the first half of the journey, and travels at an average speed of \(75\) km/h for the second half of the journey, find in km/h the average speed of this car of its whole journey from City A to City B.

Aini drives from City A to City B via the same highway. Given that she drives at an average speed of \(90\) km/h for \(2\) hours, then she takes a break for \(y\) hours, and continued driving at an average speed of \(80\) km/h for \(z\) hours until she arrives in City B.

3. Using your answers in (i), find the value of \(z\).
4. Given that the average speed of Aini’s whole journey from City A to City B is \(75\) km/h, find the value of \(y\), i.e., the number of hours she spends taking a break.