Tractor 17

A tractor's average speed was 2.4 km/h in the first minute of starting, 3.6 km/h in the second and third minutes, and 5.0 km/h in the fourth through sixth minutes. What distance did it cover during the first six minutes of driving? Determine the tractor's average speed over this time.

Final Answer:

v =  4.1 km/h

Step-by-step explanation:

$$\begin{gathered} t_1=1\text{min}\to \text{h}=1:60\text{h}=0.01667\text{h} \\ {v}_1=2.4\text{km/h} \\ {t}_2=2\text{min}\to \text{h}=2:60\text{h}=0.03333\text{h} \\ {v}_2=3.6\text{km/h} \\ {t}_3=3\text{min}\to \text{h}=3:60\text{h}=0.05\text{h} \\ {v}_3=5.0\text{km/h} \\ {s}_1=v_1\cdot t_1=2.4\cdot 0.0167=\frac{1}{25}=0.04\text{km} \\ {s}_2=v_2\cdot t_2=3.6\cdot 0.0333=\frac{3}{25}=0.12\text{km} \\ {s}_3=v_3\cdot t_3=5\cdot 0.05=\frac{1}{4}=0.25\text{km} \\ s=s_1+s_2+s_3=0.04+0.12+0.25=\frac{41}{100}=0.41\text{km} \\ t=t_1+t_2+t_3=0.0167+0.0333+0.05=\frac{1}{10}=0.1\text{h} \\ v=\frac{s}{t}=\frac{0.41}{0.1}=4.1\text{km/h} \end{gathered}$$

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