Minutes ticking

There are $\frac {24}{3} = 8$ hours in a third of the day. There are $50\% \times 8 = 4$ hours in $50\%$ of a third of the day. Hence, there are $4 \times 60 = 240$ minutes in the specified time period.

Note: This problem would be easier to proceed if you converted from hours to minutes at the last step, instead of finding the number of minutes in a day.