Tourist Jirka

The distance between points A and B is 13.5 km. Jirka went from point A to point B at an unknown speed and for an unknown period. Back to point A, it went slower by 3 km/h, meaning it went 20 minutes more.

How long does Jirka take the return journey?

Correct answer:

t₂ =  1.4 h

Step-by-step explanation:

$$\begin{gathered} 13.5=v_1{t}_1 \\ 13.5=v_2{t}_2=(v_1-3)(t_1+20/60) \\ 3x^2+x-4.5=0 \\ a=3;b=1;c=-4.5 \\ D=b^2-4ac=1^2-4\cdot 3\cdot (-4.5)=55 \\ D>0 \\ {x}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{-1\pm \sqrt{55}}{6} \\ {x}_{1,2}=-0.166667\pm 1.236033 \\ {x}_1=1.069366415 \\ {x}_2=-1.402699748 \\ \text{ Factored form of the equation: } \\ 3(x-1.069366415)(x+1.402699748)=0 \\ {t}_1=x_1=1.0693664145159h \\ {t}_2=t_1+20/60=1.4\text{h} \\ {v}_1=13.5/t_1=12.62km/h \\ {v}_2=13.5/t_2=9.62km/h \end{gathered}$$

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