Two cars

Two cars (trucks and passenger) drove simultaneously from two places 50 km away. If they go against each other, they will meet in 30 minutes. If they follow each other in the same direction, the car will catch up with the truck in 2.5 hours. What is the speed of each of them?

Correct answer:

v₁ =  40 km/h
v₂ =  60 km/h

Step-by-step explanation:

$$\begin{gathered} s=50\text{ km } \\ {t}_1=30\text{ min}\to \text{ h}=30\mathrm{/}60\text{ h}=0.5\text{ h } \\ {t}_2=2.5\text{ h } \\ {v}_1\cdot t_1+v_2\cdot t_1=s \\ {v}_2\cdot t_2-v_1\cdot t_2=s \\ {v}_1\cdot 0.5+v_2\cdot 0.5=50 \\ {v}_2\cdot 2.5-v_1\cdot 2.5=50 \\ 0.5v_1+0.5v_2=50 \\ 2.5v_1-2.5v_2=-50 \\ {v}_1=40=40\text{ km/h } \\ {v}_2=60 \end{gathered}$$

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