Ships

At 0:00, a ship set sail at 22 km/h. At 9:00, a sailboat followed at 43 km/h. When does the sailboat catch up with the ship?

How many minutes will it take for the sailboat to catch up?

Result

t = 18:26 hh:mm
m =  565.7 min

Step-by-step explanation:

$$\begin{gathered} t_1=0:00=0hr00min=0+\frac{00}{60}=0hr=0 \\ {v}_1=22\text{km/h} \\ {t}_2=9:00=9hr00min=9+\frac{00}{60}=9hr=9 \\ {v}_2=43\text{km/h} \\ {s}_1=s_2 \\ {v}_1\cdot (x-t_1)=v_2\cdot (x-t_2) \\ 22\cdot (x-0)=43\cdot (x-9) \\ 21x=387 \\ x=\frac{387}{21}=18.42857143 \\ x=\frac{129}{7}\doteq 18.428571 \\ t=x=18.4286=18.42857=18:26\text{hh}:\text{mm} \end{gathered}$$

$$\begin{gathered} T=x-t_2=18.4286-9=\frac{66}{7}\doteq 9.4286\text{h} \\ m=T\to \text{min}=T\cdot 60\text{min}=9.4286\cdot 60\text{min}=565.7\text{min}=565.7\text{min} \end{gathered}$$

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