Day trip

A group of tourists went on a day trip. For two hours they walked at a speed of 6 km/h, for another hour they climbed a steep hill at a speed of 2 km/h, spent an hour and a half at lunch, then in an hour they inspected the castle garden at a free step at a speed of 1 m/s and finally for three hours they returned home at speed 4. km/h.
a) Calculate the total time tourists spend on the trip.
b) Calculate their average speed.

Correct answer:

t =  8.5 h
v =  3.4824 km/h

Step-by-step explanation:

$$\begin{gathered} t_1=2\text{h} \\ {v}_1=6\text{km/h} \\ {t}_2=1\text{h} \\ {v}_2=2\text{km/h} \\ {t}_3=1.5\text{h} \\ {v}_3=0\text{km/h} \\ {t}_4=1\text{h} \\ {v}_4=1\text{m/s}\to \text{km/h}=1\cdot 3.6\text{km/h}=3.6\text{km/h} \\ {t}_5=3\text{h} \\ {v}_5=4\text{km/h} \\ t=t_1+t_2+t_3+t_4+t_5=2+1+1.5+1+3=8.5\text{h} \end{gathered}$$

$$\begin{gathered} s_1=v_1\cdot t_1=6\cdot 2=12\text{km} \\ {s}_2=v_2\cdot t_2=2\cdot 1=2\text{km} \\ {s}_3=v_3\cdot t_3=0\cdot 1.5=0\text{km} \\ {s}_4=v_4\cdot t_4=3.6\cdot 1=\frac{18}{5}=3.6\text{km} \\ {s}_5=v_5\cdot t_5=4\cdot 3=12\text{km} \\ s=s_1+s_2+s_3+s_4+s_5=12+2+0+3.6+12=\frac{148}{5}=29.6\text{km} \\ v=s/t=29.6/8.5=3.4824\text{km/h} \end{gathered}$$

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