On a journey of 80km, a car covers the first 40km with a uniform of 80km/hr. how fast it should travel in the next 40km so that an average speed of 100km/hr is maintained for the entire journey?

Explanation

Let total distance 2s=80km
Time taken to cover a distance s with a speed `v_(1)` is
`t_(2)=(s)/(v_(1))`
Let `v_(2)` be the speed of the car in the next 40 km of journey Then, time taken to cover another 40km with a speed `v_(2)` is
`t_(2)=(s)/(v_(2))`
Average speed over entire journey is given by
`v_("av")=(2s)/(t_(1)+t_(2))=(2s)/((s)/(v_(1))+(s)/(v_(2)))=(2s)/(s((1)/(v_(1))+(1)/(v_(2))))`
`=(2v_(1)v_(2))/(v_(1)+v_(2))`
Given, `v_("av")=100` km/hr
and `v_(1)=80` km/hr
`therefore 100=(2xx80xxv_(2))/(80+v_(2))`
`rArr 80+v_(2)=(160v_(2))/(100)`
`rArr 80+v_(2)=1.6v_(2)`
OR `0.6v_(2)=80`
`rArr v_(2)(80)/(0.5)=133.3` km/hr