Distance 8080

The driver covered the distance between the two cities in 2 hours at an average speed of 75 km/h. How does he have to change speed to get 20 minutes faster?

Correct answer:

v₂ =  90 km/h
d =  15 km/h

Step-by-step explanation:

$$\begin{gathered} v_1=75\text{km/h} \\ t=2\text{h} \\ s=v_1\cdot t=75\cdot 2=150\text{km} \\ {t}_2=t-\frac{20}{60}=2-\frac{20}{60}=\frac{2\cdot 60}{60}-\frac{20}{60}=\frac{120}{60}-\frac{20}{60}=\frac{120-20}{60}=\frac{100}{60}=\frac{5}{3}\doteq 1.6667\text{h} \\ {v}_2=s/t_2=150/\frac{5}{3}=150:\frac{5}{3}=150\cdot \frac{3}{5}=\frac{150\cdot 3}{5}=\frac{450}{5}=90\text{km/h} \end{gathered}$$

$d=v_2-v_1=90-75=15\text{km/h}$

Try another example