Question

The distance between delhi and agra is 200km. 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?

Answer 1

d1+d2/1+100/x

70=100+100/1+100/x
70(x+100/x)=200
70(x+100)=200x
x+100=200x/770
x+100=20x
x=20x-100/7
x=80x/7

Answer 2

Here,

Total distance

= 200 km

Average speed

= 70 km/h

Total taken time :-

= Total distance/Average speed

= 200/70

= 20/7 hour

1st part of Journey :-

Distance = 100 km

Speed = 50 km/h

Now,

Time taken,

t1 = 100/50

t1 = 2 hour

Now

2nd part Journey,

Distance = 100 km

Here,

Speed = p km/h

Time taken,

t2 = (100/p) hour

So,

t1 + t2 = 20/7

2 + (100/p) = 20/7

p = 116.6 km/h