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the distance between Delhi and Agra is 200 km . A train travels the first 200 km at a speed of 100 km/h . How fast must the train travel the

Home/Math/the distance between Delhi and Agra is 200 km . A train travels the first 200 km at a speed of 100 km/h . How fast must the train travel the

the distance between Delhi and Agra is 200 km . A train travels the first 200 km at a speed of 100 km/h . How fast must the train travel the

Question

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

## Answers ( )

Distance = 100 km

Speed = 50 km/h

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

Average speed = Total distance traveled/ Total time taken

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

For the first part:

Distance = 100 km

Speed = 50 km/h

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

For the second part:

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

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

Answer:200/100 +100/x =300/70

Time equal

2+100/x=30/7

100/x=30/7-2

100/x=16/7

x=7*100/16

x=7*6.25

x=43.75 km