Question

A boy runs for 10 min at a uniform speed of 9 km/hr.At what speed should he run for next 20 min so that the average speed comes 12 km/hr.?

Answer 1

Distance covered in 10 minutes = 9 km 10/60 hrs = 1.5 km
Speed for the 2nd leg = V kmph 
Distance coveed in 2nd leg = V * 20/60 = V / 3    km

Overall average speed = total distance / total time = 
        ( 1.5 + V/3 ) /   (10+20)/60  = 12  km ph

   2 (1.5 + V/3) = 12
  1.5 + V/3 = 6
  V = 13.5 KMPH

Answer 2

given , 
time1 = 10 min = 1/6 h
time2 = 20 min = 1/3 h
speed1 = 9 km/h 
speed2 = x km/h
distance1 = s * t = 1/6 * 9 =1.5 km
distance2 = s * t = x * 1/3 = 1/3x 
average speed = 12 km/h
therefore , 
av.velocity = total displacement / total time 
12 = (1.5 + 1x/3 ) / 1/6 + 1/3
12 = ( 15/10 + 1x/3 ) / 1/2 
12 = ( 15/10 + 1x/3 ) 2 
12 = 30 / 10 + 2x / 3 
12 = 3 + 2x/3 
12 - 3 = 2x/3 
9 = 2x/3 
9 * 3 = 2 x
27 / 2 = x
13.5 = x 
therefore the answer is 13.5 km/h .
           i hope it helps...........................^_^