Buses to cover a distance of 72 km in 1.5 hours over the first 36 km it travels at a speed of 54 km per hour at what speed must it travel for the rest of the distance in order to complete the journey in the time
The correct answer and explanation is:
To solve this problem, we need to determine the speed the bus must travel for the remaining 36 km after covering the first 36 km at 54 km per hour.
Step 1: Calculate the time taken to travel the first 36 km
The formula for time is: Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}
For the first 36 km, the speed is 54 km per hour. Therefore, the time taken to travel the first 36 km is: Time=36 km54 km/h=0.6667 hours≈40 minutes\text{Time} = \frac{36 \text{ km}}{54 \text{ km/h}} = 0.6667 \text{ hours} \approx 40 \text{ minutes}
Step 2: Determine the remaining time
The total time for the entire journey is 1.5 hours. The time spent covering the first 36 km is approximately 0.6667 hours. Therefore, the remaining time to cover the next 36 km is: Remaining time=1.5 hours−0.6667 hours=0.8333 hours≈50 minutes\text{Remaining time} = 1.5 \text{ hours} – 0.6667 \text{ hours} = 0.8333 \text{ hours} \approx 50 \text{ minutes}
Step 3: Calculate the required speed for the remaining 36 km
Now, we use the formula for speed: Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}
For the remaining 36 km, the time available is 0.8333 hours. The required speed is: Speed=36 km0.8333 hours=43.2 km/h\text{Speed} = \frac{36 \text{ km}}{0.8333 \text{ hours}} = 43.2 \text{ km/h}
Conclusion:
The bus must travel at a speed of 43.2 km per hour for the remaining 36 km to complete the journey in 1.5 hours.