A motorist do does the first part of his journey at an average speed of 54km/h. Then he increases the speed to 60km/h for the rest of the journey. If he travels 225km in 4 hours, what is the distance traveled for the rest of his journey? show clear steps.

54 T1 + 60 T2 = 225 (km)

T1 + T2 = 4 (hours)
54 T1 + 54 T2 = 216
6 T2 = 9
T2 = 1.5 hours
T1 = 2.5 hours
60 T2 = 90 km is travelled at the higher speed.

To find the distance traveled for the rest of the journey, we need to subtract the distance traveled at the average speed from the total distance of the journey.

Let's break down the information we have:
- The motorist traveled at an average speed of 54 km/h for the first part of the journey.
- The motorist increased the speed to 60 km/h for the rest of the journey.
- The total distance traveled is 225 km.
- The total time taken is 4 hours.

Step 1: Find the distance traveled at the average speed.
To calculate the distance traveled at the average speed, we can use the formula:
Distance = Speed x Time

For the first part of the journey, the time taken is T1 hours (unknown), and the average speed is 54 km/h.
So, the distance traveled at the average speed is:
Distance1 = 54 km/h x T1 hours = 54T1 km

Step 2: Find the distance traveled for the rest of the journey.
To find the distance traveled for the rest of the journey, we subtract the distance traveled at the average speed from the total distance.
Distance2 = Total distance - Distance1

Since the total distance is given as 225 km, we have:
Distance2 = 225 km - (54T1) km

Step 3: Find the time taken for the rest of the journey.
We know that the total time taken is 4 hours, and the time taken at the average speed is T1 hours. So, the time taken for the rest of the journey is:
T2 = Total time - T1

Since the total time is given as 4 hours, we have:
T2 = 4 hours - T1

Step 4: Find the distance traveled for the rest of the journey using the time and speed.
Now that we have the time and speed for the rest of the journey, we can calculate the distance traveled using the formula:
Distance = Speed x Time

For the rest of the journey, the time taken is T2 hours (from Step 3), and the speed is 60 km/h.
So, the distance traveled for the rest of the journey is:
Distance2 = 60 km/h x T2 hours = 60T2 km

Step 5: Substitute the value of T2 from Step 3 into the equation for Distance2.
Distance2 = 60T2 km = 60(4 - T1) km

Therefore, the distance traveled for the rest of the journey is 60(4 - T1) km.