Two towns

X and Y are two towns . A man goes from town X to town Y at an average speed of 30 km/h and returns at the average speed 20 km/h. Find the distance between the two towns if the man takes 10 hours on the whole.

Final Answer:

s =  120 km

Step-by-step explanation:

$$\begin{gathered} v_1=30\text{km/h} \\ {v}_2=20\text{km/h} \\ t=10\text{h} \\ {t}_1=s/v_1 \\ {t}_2=s/v_2 \\ {t}_1+t_2=t \\ s/v_1+s/v_2=t \\ s/30+s/20=10 \\ 5s=600 \\ s=\frac{600}{5}=120=120\text{km} \\ s=120 \\ \text{ Verifying Solution: } \\ {t}_1=s/v_1=120/30=4\text{h} \\ {t}_2=s/v_2=120/20=6\text{h} \end{gathered}$$

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