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

Time, speed, and distance are related using the equation: Distance = Speed × Time.

## Answer: The train must travel at a speed of 116.67 km/h for the next 100km so that the average speed for the whole journey is 70km/h.

To find the average speed we need to use the relation:

**Average speed = Total distance traveled/ Total time taken**

Let's now consider the conditions given in the question to find the required value.

**Explanation:**

Let's find the time taken by train to travel each part of the distance.

For the first 100 km:

Distance = 100 km

Speed = 50 km/h

Time = Distance/Speed = 100/50 = 2 h

For the second(next) 100 km:

Let the speed of the train be 's' km/h

Distance = 100 km

Time = Distance/Speed = 100/s

Now, as we know that:

Average speed = Total distance traveled/ Total time taken

where, Average speed = 70 km/h

Total distance travelled = 200 km

Total time taken = 2 + 100/s

Substituting these values in the average speed equation, we get:

Average speed = Total distance traveled/ Total time taken

or, 70 = 200/ (2 + 100/s)

or, 70 × (2 + 100/s) = 200

or, 140 + 7000/s = 200

or, 7000/s = 60

or, s = 7000/60 = 116.67 km/h

### Therefore, the speed of the train must be 116.67 km/h.

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