$\text{we can solve by using weighted average concept,here speed acts like average and time acts like weights}$
$time=\frac{distance}{speed}$
$\text{the ratio of times can by found by multiplying distance ratios and inverse of speeds ratios}$
$distance ~ratio= \frac12:\frac14:\frac14 = 2:1:1$
$inverse~ of ~speed ~ratio= \frac1{60}:\frac1{30}:\frac1{10} = 1:2:6$
$\text{times ratio = (2:1:1)*(1:2:6)=2:2:6=1:1:3} ~and~ speeds ~are~ 60,30,10$
$\text{now average speed=} \frac{1*60+1*30+3*10}{1+1+3}=\frac{120}5=24$