Warehouse cars

From the warehouse started truck at speed 40km/h. After 1hour 30mins started from the same place same direction a car at speed 70 km/h. For how long and at what distance from the warehouse overtake a truck?

Correct answer:

t =  2 h
s =  140 km

Step-by-step explanation:

$$\begin{gathered} t_1=1{\displaystyle \frac{30}{60}}=1+{\displaystyle \frac{30}{60}}={\displaystyle \frac{1\cdot 60+30}{60}}={\displaystyle \frac{90}{60}}={\displaystyle \frac{3}{2}}=1.5\text{ h } \\ {v}_1=40\text{ km/h } \\ {v}_2=70\text{ km/h } \\ s=v_1\cdot (t+t_1) \\ s=v_2\cdot t \\ s=40\cdot (t+1.5) \\ s=70\cdot t \\ s-40t=60 \\ s-70t=0 \\ s=140 \\ t=2=2\text{ h} \end{gathered}$$

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