I rode one-third of a journey at 10 km an hour, one-third more at 9, and the rest at 8 km an hour; if I had ridden half the journey at 10, and the other half at 8 km per hour, I should have been half a minute longer on the way. I ride for x distance. Then x is :

Explanation

Time taken in first case `T_1 = x/(3*10)+x/(3*9)+x/(3*8) = x/30+x/27+x/24`

Time taken in second case `T_2 = x/(2*10)+x/(2*8) = x/20+x/16`

Now, we are are given, difference between `T_2` and `T_1` is `1/2` minute or `1/120` hour.

`:. x/20+x/16-x/30-x/27-x/24 = 1/120`

`=>(x(108+135-72-80-90))/2160 = 1/120`

`=>x = 2160/120 km`

`x = 18km`