Question

A car has to travel 200 km. If it travels first 100 km with the speed of 60 km/h, then what should the speed of next 100 km be to have an average speed of 80 km/h for the entire journey?

Answer 1

S = 200 km
time duration to travel first 100 km = 100/60 = 5/3 hours
speed for next 100 km = v kmph
duration for the next 100 km :   100/v  hours

average speed = 80 kmph = 200 km / [ 5/3 + 100/v ] hrs
so      80 [5/3 + 100/v ] = 200

solving this :  we get   v = 120 kmph

Answer 2

a car travels = 200 km
first km. covered by car = 100 km.
so, 100/60 = 5/3 hours
speed of next 100 km be = v kmph
then, duration of next 100 km be. = 100/v
now average speed = 80 kmph = 200km/(5/3+100/v) hours

then, it will come:
80(5/3+100/v) = 200
= 120 kmph

hence it is proved that v is 120 kmph.