Siblings 6

Siblings Martin and Judy decided to visit a castle that is 10 km away from their home. Martin left at 7:30 and walked at a speed of 4 km/h. Judy rode her bicycle behind him an hour and a half later and rode at a speed of 16 km/h. Did Judy catch up with Martin before the castle? If so, what time was it and how far from the castle?

Result

x =  2 km
t₃ = 9:30 hh:mm

Step-by-step explanation:

$$\begin{gathered} s=10\text{km} \\ {t}_1=7:30=7hr30min=7+\frac{30}{60}=7.5hr=7.5 \\ {t}_2=1.5\text{h} \\ {v}_1=4\text{km/h} \\ {v}_2=16\text{km/h} \\ {s}_1=s_2 \\ {v}_1\cdot (t+t_2)=v_2\cdot t \\ 4\cdot (t+1.5)=16\cdot t \\ 12t=6 \\ t=\frac{6}{12}=0.5 \\ t=\frac{1}{2}=0.5 \\ {s}_1=v_2\cdot t=16\cdot 0.5=8\text{km} \\ {s}_1<s \\ x=s-s_1=10-8=2\text{km} \end{gathered}$$

$t_3=t_1+t+t_2=7.5+0.5+1.5=\frac{19}{2}=9.5=9:30\text{hh}:\text{mm}$

Try another example