25. A boy tode a bike and covered 90 km at an average spees first thirty km in two hours. What is average \( 36 \mathrm{~km} / \mathrm{h} \) but he covered fored speed at which remaining distance was covered?

To find the average speed at which the remaining distance was covered, we first need to determine the total time taken for the entire journey and then the time taken for the remaining distance. 1. **Distance and Time for the First Part:** - Distance covered: 30 km - Time taken: 2 hours - Average speed for the first part: \( \frac{30 \text{ km}}{2 \text{ hours}} = 15 \text{ km/h} \) 2. **Total Distance:** - Total distance to be covered: 90 km 3. **Remaining Distance:** - Remaining distance after the first part: \( 90 \text{ km} - 30 \text{ km} = 60 \text{ km} \) 4. **Total Time for the Journey:** - Average speed for the entire journey is given as \( 36 \text{ km/h} \). - Total time for the entire journey: \[ \text{Total time} = \frac{\text{Total distance}}{\text{Average speed}} = \frac{90 \text{ km}}{36 \text{ km/h}} = 2.5 \text{ hours} \] 5. **Time Taken for the Remaining Distance:** - Time taken for the first part: 2 hours - Therefore, time taken for the remaining distance: \[ \text{Time for remaining distance} = \text{Total time} - \text{Time for first part} = 2.5 \text{ hours} - 2 \text{ hours} = 0.5 \text{ hours} \] 6. **Average Speed for the Remaining Distance:** - Average speed for the remaining distance: \[ \text{Average speed} = \frac{\text{Remaining distance}}{\text{Time for remaining distance}} = \frac{60 \text{ km}}{0.5 \text{ hours}} = 120 \text{ km/h} \] Thus, the average speed at which the remaining distance was covered is **120 km/h**.