Oversized 53431

Behind the vehicle with an oversized load, which moves at an average speed of 16 km/h, they sent a second escort vehicle 2.5 hours later, which travels at an average speed of 70 km/h. At what time and at what distance does this vehicle reach the oversized load?

Correct answer:

t =  0.7407 h
s =  51.8519 km

Step-by-step explanation:

$$\begin{gathered} v_1=16\text{km/h} \\ T=2.5\text{h} \\ {v}_2=70\text{km/h} \\ {s}_1=s_2=s \\ {v}_1\cdot (t+T)=v_2\cdot t \\ 16\cdot (t+2.5)=70\cdot t \\ 54t=40 \\ t=\frac{40}{54}=0.74074074 \\ t=\frac{20}{27}\doteq 0.740741=0.7407\text{h} \end{gathered}$$

$$\begin{gathered} s=v_2\cdot t=70\cdot 0.7407=\frac{1400}{27}\doteq 51.8519\text{km} \\ \text{ Verifying Solution: } \\ {s}_1=v_1\cdot (t+T)=16\cdot (0.7407+2.5)=\frac{1400}{27}\doteq 51.8519\text{km} \\ {s}_1=s \end{gathered}$$

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