Question

the distance between 2 station is 200 km. A train travels for the first 100 KM at a speed of 50 km per hour. how fast should the train travel the next 100 KM so as it will have average of 70 km per hour for the whole journey

Answer 1

average speed= total distance/total time taken
time taken for the first 100km = distance/speed
                                                =100/50
                                               =  2hr   
70 km/hr=200/2+t2
140 +70t2 =200
70t2=60
t2 = 60/70= 6/7 hrs
speed= distance/time
             =100/6/7
             = 700/6
             =116.6km/hr

Answer 2

The total distance =200km
Let the total time be't' hours
Speed of the train for the first 100km is 50 km/ h

Time taken for the first 100km (t1)= 100km/ 50km /h= 2 h
Average speed = total distance / total time taken
=total distance (s1+s2)/ total time 2(t1+t2)
Where s2= next 100km travelled by train.

t2= time taken to travel next 100km

70km/h=200km/ (2+t2)h
70= 200/2+t2
t2=6/7h
Therefore speed required by train to travel next 100 km. So as to attain 70km/h .
Average speed is(v2)= distance / time
=100km/6/7
=700/6
=116.67km/h