Makarska riviera

The motor boat departs from Baška Voda at 19:15 and arrives in Makarska at an average speed of 30 km/h at 20:00. However, a group of tourists from Germany must be in Makarska a third of the time earlier. What should the average speed of the boat be?

Correct answer:

v₂ =  45 km/h

Step-by-step explanation:

$$\begin{gathered} t_1=19:15=19hr15min=19+\frac{15}{60}=19.25hr=19.25 \\ {t}_2=20:0=20hr0min=20+\frac{0}{60}=20hr=0.5 \\ {v}_1=30\text{km/h} \\ t=t_2-t_1=0.5-19.25=\frac{3}{4}=0.75\text{h} \\ s=v_1\cdot t=30\cdot 0.75=\frac{45}{2}=22.5\text{km} \\ {t}_2=t-t/3=0.75-0.75/3=\frac{1}{2}=0.5\text{h} \\ {v}_2=\frac{s}{t_2}=\frac{22.5}{0.5}=45\text{km/h} \end{gathered}$$

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