Adam reaches

If Adam walks at 3 km/h, he will reach school 15 minutes late. If he walks at 4 km/h (kmph), he will reach school 15 minutes earlier than usual. What is the distance between school and house?

Final Answer:

x =  6 km

Step-by-step explanation:

$$\begin{gathered} t_1=0:15=0hr15min=0+\frac{15}{60}=0.25hr=0.25 \\ {v}_1=3\text{km/h} \\ {t}_2=0:15=0hr15min=0+\frac{15}{60}=0.25hr=0.25 \\ {v}_2=4\text{km/h} \\ x=s_1=s_2 \\ x=v_1\cdot (t+t_1) \\ x=v_2\cdot (t-t_2) \\ {v}_1\cdot (t+t_1)=v_2\cdot (t-t_2) \\ 3\cdot (t+0.25)=4\cdot (t-0.25) \\ t=1.75 \\ t=\frac{1.75}{1}=1.75 \\ t=\frac{7}{4}=1.75 \\ x=v_1\cdot (t+t_1)=3\cdot (1.75+0.25)=6\text{km} \end{gathered}$$

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