1.

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 get average 70 Km/h for the whole journey

Answer»

Average SPEED = Total DISTANCE travelled / Total time taken
so, 70 = 200 / Total time taken
and, Total time taken = 200 / 70 = 2.85 hours......(1)
For the first part of the journey:
speed = 50km/h
distance = 100km
time = ?
speed = distance travelled / time taken
so, 50 = 100 / time taken
and, time taken = 100/50 = 2 hours........(2)
For the second part of the journey:
speed = x km/h (supposed)
distance = 100 km
time = ?
speed = distance travelled / time taken
so, x = 100 / time taken
and, time taken = 100/x .......(3)
Now, adding equations (2) and (3) , we get the total time taken for the ENTIRE trip:
total time taken = 2+ 100/x.....(4)
we ALREADY know that the total time taken for the trip is 2.85 hours from equation (1). So, comparing equations (4) and (1) , we get:
2+ 100/x = 2.85
100/x = 2.85 - 2
100/x = 0.85
x = 0.85*100
x = 85 km/h
Thus, the train should travel the next 100 km distance at a speed of 85 km/h.


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