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 ?

A motorcyclist covers 1/3 of a given distance with a speed of 10 kmh ^

1.	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 ?
Answer» Solution :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)`