A partical moves from `A` to `B` for the first one-third with speed `v_(1)` and the next two-third time with speed `v_(2)`. Find the average speed.

Explanation

Let `t_(0)` be the total time of journey.

`A` to `C`: `d_(1)=v_(1)t_(0)/3`
`C` to `B`: `d_(2)=v_(2)(2t_(0))/3`
Average speed `=(d_(1)+d_(2))/t_(0)=(t_(0)(v_(1)/3+(2v_(2)))/2)/t_(0)`
`=(v_(1)+2v_(2))/3`