In order to calculate the distance travelled in one hour, we can divide the total number of miles by the amount of time required for that number of miles:
[tex]\text{speed}=\frac{78}{2\frac{2}{3}}=\frac{78}{(2+\frac{2}{3})}=\frac{78}{\frac{6}{3}+\frac{2}{3}}=\frac{78}{\frac{8}{3}}=78\cdot\frac{3}{8}=\frac{39\cdot3}{4}=\frac{117}{4}[/tex]So in one hour, the distance travelled is 117/4 miles.
Converting this value into a mixed number, we have:
[tex]\frac{117}{4}=\frac{116}{4}+\frac{1}{4}=29+\frac{1}{4}=29\frac{1}{4}[/tex]--------
Done!
Do you have any questions about the answer?