# On a 120 km long track, a train travels the first 30 km with a uniform speed of 30 km/h. How fast must the train travel for the rest part of the journey so as to average 60 km/h for the entire trip?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

On a 120 km long track, a train travels the first 30 km with a uniform speed of 30 km/h. How fast must the train travel for the rest part of the journey so as to average 60 km/h for the entire trip?

A train must travel with a uniform speed of 90 km/h to cover the rest 60 km. To evaluate the average speed of the train the total distance covered by the train needs to be divided by the total time taken by the train. Average Speed is commonly expressed in units such as kilometers per hour (km/h) or meters per second (m/s).

## Average Speed Of The Train

Average speed is a measure of the overall rate at which an object or person has covered a certain distance over a given period of time. It is calculated by dividing the total distance traveled by the total time taken.

Average Speed = Total Distance / Total Time

For example, if a car travels 200 kilometers in 4 hours, the average speed would be:

Average Speed = 200 km / 4 hours = 50 km/h

Average speed provides an indication of how fast or slow an object or person is moving on average, considering the entire journey. It is important to remember that average speed does not provide information about the specific variations in speed during the travel; it represents an overall measure of the rate of travel over the entire duration.

Solution

We need to calculate the time it takes for the train to travel the first 30 km and the remaining 90 km.

Let’s denote the speed of the train for the remaining part as v km/h.

Time taken to travel the first 30 km:

Time = Distance / Speed

Time = 30 km / 30 km/h

Time = 1 hour

Now, let’s calculate the time taken to travel the remaining 90 km:

Time = Distance / Speed

Time = 90 km / v km/h

Time = 90/v hours

The total time taken for the entire trip is the sum of the time taken for the first 30 km and the time taken for the remaining 90 km:

Total Time = 1 hour + 90/v hours

Total Time = (v + 90)/v hours

To average 60 km/h for the entire trip, the total time taken should be:

Total Time = Total Distance / Average Speed

Total Time = 120 km / 60 km/h

Total Time = 2 hours

Setting the two expressions for the total time equal to each other:

(v + 90)/v = 2

Now, let’s solve this equation for v:

(v + 90) = 2v

90 = v

Therefore, the train must travel the remaining part of the journey at a speed of 90 km/h in order to average 60 km/h for the entire trip.

Summary

## On a 120 km long track, a train travels the first 30 km with a uniform speed of 30 km/h. How fast must the train travel for the rest part of the journey so as to average 60 km/h for the entire trip?

On a 120 km long track, a train travels the first 30 km with a uniform speed of 30 km/h. The train must travel 90 km/hr for the rest part of the journey to an average of 60 km/h for the entire trip.

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