Question

On a 120km track, a train travels the first 30 km at a uniform speed of 30 km/hr. How fast

must the train travel the next 90 km so as to average 60 km/hr for the entire trip?

Answer 1

hello friend
given that, total distance covered , S = 120km
first 30 km is covered at 30 km/hr 
time taken is t1 = 30 /30 = 1 hr
let the train cover next 90 km at speed x km/hr
let the time is t2  = 90/x hours .
average speed = total distance/total time
= 60= 120 / (t1 + t2)  
= 60 = 120 / ( 1+90/x )
= 1+ 90/x =2
= 90/x = 1
= x = 90km/hr 
thus to achieve an average speed of 60km/hr the train must travel the next 90 km at 90 km/hr .

hope this helps ..

Answer 2

Hello !

Speed for first 30 km = 30 km/hr
Speed for next 90 km = x

time = 2 hrs

average speed = 30 + x / 2

60 = 30 + x /2

120 = 30 + x 

x = 120 - 30
   = 90 km/hr

He must travel with a speed of 90 km/hr for the next 90 km