Journey to spa

Mr. Dvorak took his wife to the spa and the journey took 3.5 hours. On the way back, he drove 12 km/h faster and was home in 3 hours. At what speed did he go to the spa and at what speed did he return?

Correct result:

v₁ =  72 km/h
v₂ =  84 km/h

Solution:

$$\begin{gathered} s=v_1\cdot t_1=v_2\cdot t_2 \\ {t}_1=3.5\text{ h } \\ {t}_2=3\text{ h } \\ {v}_1\cdot t_1=v_2\cdot t_2 \\ {v}_2=v_1+12 \\ {v}_1\cdot 3.5=v_2\cdot 3 \\ {v}_2=v_1+12 \\ 3.5v_1-3v_2=0 \\ {v}_1-v_2=-12 \\ {v}_1=72=72\text{ km/h } \\ {v}_2=84 \end{gathered}$$

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