On a 120km track,a train travels the first 30km at a uniform speed of 30km/hr.how fast must the train travel the next 90km so as to average 60km/hr for the entire trip?

The train travelled 30km at 30km/hr. It took therefore 30/30=1 hr.

To attain an average of 60km per hour over 120 km, the total time must be 120/60=2 hours.
There is (2-1)=1 hour left to do the remaining 90km. What should be the speed?

120

To find out how fast the train must travel the next 90km in order to average 60km/hr for the entire trip, we can use the concept of average speed.

Average speed is defined as the total distance traveled divided by the total time taken.

We are given that the train travels the first 30km at a uniform speed of 30km/hr. Therefore, the time taken to cover the first 30km can be found using the formula:

Time = Distance / Speed

So, the time taken to cover the first 30km is:

Time = 30km / 30km/hr = 1 hour

Now, let's calculate the time taken to cover the remaining 90km (x) at the required average speed of 60km/hr.

The total distance traveled in the entire trip is 120km. Considering the first 30km already covered, the remaining distance is 90km.

Now, let's calculate the time taken to cover the remaining 90km at the average speed of 60km/hr:

Time = Distance / Speed

Time = 90km / 60km/hr = 1.5 hours

Since total time taken is the sum of the time taken for each segment of the trip, we can set up an equation:

Total Time = Time for 30km + Time for 90km

1 hour + 1.5 hours = 2.5 hours

Now, we can use the formula for average speed to find the required speed for the second segment:

Average Speed = Total Distance / Total Time

60km/hr = 120km / 2.5 hours

To find the speed at which the train must travel for the next 90km, we can rearrange the equation:

Speed = Distance / Time

Speed = 90km / 1.5 hours

Therefore, the train must travel at a speed of 60 km/hour for the next 90 km in order to average 60 km/hour for the entire trip.