Warehouse cars

From the warehouse, a truck started at a speed of 40km/h. After 1 hour 30 mins started from the same place in the same direction a car at 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:

$$\begin{gathered} t_1=1\frac{30}{60}=1+\frac{30}{60}=\frac{1\cdot 60+30}{60}=\frac{60+30}{60}=\frac{90}{60}=\frac{3}{2}=1.5\text{h} \\ {v}_1=40\text{km/h} \\ {v}_2=70\text{km/h} \\ s=v_1\cdot (t+t_1) \\ s=v_2\cdot t \\ s=40\cdot (t+1.5) \\ s=70\cdot t \\ s-40t=60 \\ s-70t=0 \\ Row2-Row1\to Row2 \\ s-40t=60 \\ -30t=-60 \\ t=\frac{-60}{-30}=2 \\ s=60+40t=60+40\cdot 2=140 \\ s=140 \\ t=2=2\text{h} \end{gathered}$$

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