Question

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

Answer 1

Given :
The total distance= 200km
let total time be 't ' hours
speed of train for the first 100 km is 50km/h
time taken for the first 100km(t1)=distance/ speed = 100km/50km/h=2hours
Average speed=total distance/total time taken
=total distance(s1+s2)/total time(t1+t2)
where, s2= next 100km traveled by train.
t2=time taken to travel next 100km
∴70km/hr=200km/(2+t2)hours
70=200/2+t2
140+70t2=200
70t2=60
t2=60/70
t2=6/7 hours.
∴speed required by train to travel next 100km so as to attain 70km/h average speed is:
speed(v2)=distance/ time
=100km/6/7
=700/6
=116.67km/hr