Sisters

Sisters Hannah and Vera usually ride their bicycles to their grandmother's house. The journey takes Hannah 30 minutes and Vera 20 minutes. How long will it take Vera to catch up with Hannah if she starts from home five minutes later?

Final Answer:

t =  10 min

Step-by-step explanation:

$$\begin{gathered} t_1=30\text{min} \\ {t}_2=20\text{min} \\ {s}_1=s_2 \\ {v}_1\cdot (t+5)=v_2\cdot t \\ \frac{s}{t_1}\cdot (t+5)=\frac{s}{t_2}\cdot t \\ {t}_2\cdot (t+5)=t\cdot t_1 \\ 20\cdot (t+5)=t\cdot 30 \\ 10t=100 \\ t=\frac{100}{10}=10 \\ t=10=10\text{min} \end{gathered}$$

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