On a 60 km track,a train travels the first 30 km at a uniform speed of 30 km per hour. How fast the train travels the next 30km so as to have an average of 40 km per hour for the entire trip
avgvelocity= total distance/total time
total distance=60km
total time=30/30 + 30/v =(v+30)/v
40=60/(v+30)/v
= 60v/(v+30)
40v+1200=60v
v=60km/hr
To find the speed at which the train travels the next 30 km, we can use the formula for average speed:
Average speed = Total distance / Total time
First, let's find the total time taken for the entire trip. We know that the train travels the first 30 km at a speed of 30 km/h. So, the time taken to cover the first 30 km is:
Time = Distance / Speed = 30 km / 30 km/h = 1 hour
Now, let's find the total distance covered by the train in the entire trip. The track is 60 km long, so the total distance is 60 km.
Now we can plug in the values into the average speed formula:
40 km/h = 60 km / Total time
To find the total time, we rearrange the equation:
Total time = 60 km / 40 km/h = 1.5 hours
Since the first 30 km took 1 hour to cover, the remaining 30 km must be covered in the remaining time, which is 0.5 hours.
Now, to find the speed at which the train travels the next 30 km, we divide the distance by the time:
Speed = Distance / Time = 30 km / 0.5 hours = 60 km/h
Therefore, the train needs to travel the next 30 km at a speed of 60 km/h in order to have an average speed of 40 km/h for the entire trip.