Failure

Drivers of passenger cars have calculated that at a speed of 60 km/h arrives at destination within 40 minutes. After 20 km refrain five minutes due a technical failure. How fast must go the rest of the way to the finish came at the scheduled time?

Correct result:

v₂ =  80 km/h

Solution:

$$\begin{gathered} v_1=60 \\ t=40\mathrm{/}60={\displaystyle \frac{2}{3}}\doteq 0.6667\text{ h } \\ s=v_1\cdot t=60\cdot 0.6667=40\text{ km } \\ {s}_1=20\text{ km } \\ {t}_1=s_1\mathrm{/}{v}_1=20\mathrm{/}60={\displaystyle \frac{1}{3}}\doteq 0.3333\text{ h } \\ {s}_2=s-s_1=40-20=20\text{ km } \\ {t}_2=t-t_1-5\mathrm{/}60=0.6667-0.3333-5\mathrm{/}60={\displaystyle \frac{1}{4}}=0.25\text{ h } \\ {v}_2=s_2\mathrm{/}{t}_2=20\mathrm{/}0.25=80\text{ km/h} \end{gathered}$$

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