A motorcyclist covers `1/3` of a given distance with a speed of `10 kmh ^(-1) `, the next `1/3` at `20 kmh ^(-1)` and the last `1/3` at of `30 kmh^(-1).` What is the average speed of the motorcycle for the entire journey ?

Explanation

Suppose the tota distance is x.
`therefore` Time taken to cover distance `x/3` is `t _(1) = (x //3)/( 10) = (x)/(30) ` hour. Also time taken to cover next-distance `x/3 is t _(2) = (x//3)/(20) = (x)/(60)` hour, time for remaining distance `x/3` is
`t _(3) = (x//3)/(30) = (x)/(90)` hour.
`therefore` Total time to covered distance x.
`t = t _(1) + t _(2) + t _(3)`
`t = (x)/(30) + (x)/(60) + (x)/(90) = (6x + 3x + 2x )/(180) = (11x)/(180)`
`therefore` Average speed `lt v gt = (x)/(t) = (x xx 180)/(11x)= (180)/(11) kmh^(-1)`
`therefore lt v gt = (180 xx 1000)/(11 xx 3600) = (50)/(11) ms ^(-1)`