Question

if a boy runs for 10 min at uniform speed of 9km per hour.at what speed should he run for the next 20 min so that the average speed comes to 12 km per hour

Answer 1

speed of boy for 10 min =9km/h
let speed of boy for the next 20 min = x km/h
distance travelled by the boy for 10 min = 9×1/6=3/2km
distance travelled by the boy for next 20 min=x×1/3=x/3km
total time taken by the boy = 10+20 min 
                                           =30 min
                                           =1/2 h
 average speed = (3/2+x/3)/1/2
                          =((9+2x)/6)/1/2
                          =(9+2x)/3
 given, average speed = 12
⇒(9+2x)/3=12
 ⇒9+2x=36
⇒2x=36-9
⇒2x=27
⇒x=27/2
⇒x=13.5