# The distance between Delhi and Agra is 200 km. A train travels the first 100 km at a speed of 50 km/h. How fast must the train travel the next 100 km, so as to average 70 km/h for the whole journey?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The distance between Delhi and Agra is 200 km. A train travels the first 100 km at a speed of 50 km/h. How fast must the train travel the next 100 km, so as to average 70 km/h for the whole journey?

The three concepts of speed, distance, and time are related through a simple formula: speed = distance/time. This formula allows us to calculate any one of the three variables (distance, speed, or time) if we know the values of the other two.

## Distance, Speed, and Time Of The Train

Distance refers to the amount of space between two points or the length of a path traveled. It is typically measured in units like meters, kilometers, miles, or any other suitable unit of length. For example, the distance between two cities may be 100 kilometers.

Speed is the rate at which an object covers a certain distance in a given amount of time. It is a measure of how quickly something moves. Speed is usually expressed in units such as meters per second, kilometers per hour, or miles per hour. For instance, if a car travels 60 kilometers in one hour, its speed is 60 kilometers per hour.

Time is the duration or period during which an event occurs or an object is in motion. It is measured in units such as seconds, minutes, hours, or days. Time represents the progression of events from the past through the present to the future. For example, if a train journey takes 3 hours, the time taken to complete the journey is 3 hours.

Solution

Time taken by the train to travel the first 100 km

Time = Speed/Distance

100 km/ 50 km/hr = 2 hrs = t1

Let’s assume that the train travels the next 100 km at a speed of v km/hr

Hence time taken for the next 100 km

t2 = 100 km/ v km/hr = 100/v hrs

So the average speed of the whole journey

Vavg = Total distance/Total time = 100+100/ t1 + t2

= 200/2+100/v

Which is given to be 70 km/hr

200/2+100/v = 70

200 = 70(2+100/v)

= 140+7000/v

7000/v = 60

V = 7000/60

=116.67 km/hr

The average speed of the train must be 116.67 km/hr

Summary

## The distance between Delhi and Agra is 200 km. A train travels the first 100 km at a speed of 50 km/h. How fast must the train travel the next 100 km, so as to average 70 km/h for the whole journey?

The distance between Delhi and Agra is 200 km. A train travels the first 100 km at a speed of 50 km/h. The speed of the train must be 116.67 km/h for the next 100 km, so as to average 70 km/h for the whole journey.

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