Question

a boy runs for 20 min at a uniform speed 18km/h at what speed should he run for next 40 min so that his average speed be 24km/h

Answer 1

Speed of boy in first 20 min = 18 km/

As d = v × t

so, distance travelled by the boy in first 20 min

= 20/60h × 18 km/h = 6 km

let the speed for next 40 min be v km/h

so, distance travelled will be 40/60h × v kmph

= 2v/3 km

So, total distance = 6 + 2v/3 km

total time = 20 + 40 min = 60 min = 1 h

As average speed = total distance/total time

so, 24 = (6 + 2v/3)/1 = (18 + 2v)/3

or, 24×3 = 18 + 2v

or, 2v = 72 - 18 = 54

so, v = 54/2 = 27 km/h

So, he should run at a speed of 27 km/h for 40 minutes so that his average speed be 24 km/h.

Answer 2

Speed of boy in first 20 min = 18 km/

As d = v × t

so, distance travelled by the boy in first 20 min

= 20/60h × 18 km/h = 6 km

let the speed for next 40 min be v km/h

so, distance travelled will be 40/60h × v kmph

= 2v/3 km

So, total distance = 6 + 2v/3 km

total time = 20 + 40 min = 60 min = 1 h

As average speed = total distance/total time

so, 24 = (6 + 2v/3)/1 = (18 + 2v)/3

or, 24×3 = 18 + 2v

or, 2v = 72 - 18 = 54

so, v = 54/2 = 27 km/h

So, he should run at a speed of 27 km/h for 40 minutes so that his average speed be 24 km/h.