A car travels the first third of a distance with a speed of 10 kmph, the second third at 20 kmph and the last third at 60 kmph. What is its mean speed over the entire distance?

Explanation

Total distance=s,
distance travelled , `s_1=s/3`,
velocity , `v_1=10 kmph`
distance, `s_2=s/3`
velocity , `v_2=20 kmph`
distance, `s_3=s/3`
velocity , `v_3=60 kmph`
Average velocity = `(t o tal distance)/(t o tal time)`
`Time,t=t_1+t_2+t_3=s/(3v_1)+s/(3v_2)+s/(3v_3)`
( `because time = (distance)/(velocity)`)
`thereforet=s/3((v_2v_3+v_3v_1+v_1v_2)/(v_1v_2v_3))`
`=s/3[((60times20)+(60times10)+(20times10))/(60times20times10)]`
`=s/3((1200+600+200)/12000)`
`s/3 2000/12000=(2000s)/(3times12000)`
Average velocity =`s/t`
`=(s3times12000)/(2000s)`
=18 kmph