# The tourist

The tourist traveled 78km in 3 hours. Part of the journey went on foot at 6km/h, the rest of the trip by bus at 30km/h. How long did he walk?

Result

t1 =  0.5 h

#### Solution:

$s=78 \ \text{km} \ \\ t=3 \ \text{h} \ \\ v_{1}=6 \ \text{km/h} \ \\ v_{2}=30 \ \text{km/h} \ \\ \ \\ s=s_{1}+s_{2} \ \\ s=v_{1} \cdot \ t_{1}+v_{2} \cdot \ (t-t_{1}) \ \\ \ \\ \ \\ s=v_{1} \cdot \ t_{1}+v_{2} \cdot \ (t-t_{1}) \ \\ \ \\ 78=6 \cdot \ t_{1}+30 \cdot \ (3-t_{1}) \ \\ \ \\ 24t_{1}=12 \ \\ \ \\ t_{1}=\dfrac{ 1 }{ 2 }=0.5 \ \\ =\dfrac{ 1 }{ 2 }=0.5 \ \text{h} \ \\ \ \\ t_{2}=t - t_{1}=3 - 0.5=\dfrac{ 5 }{ 2 }=2.5 \ \text{h} \ \\ s_{1}=v_{1} \cdot \ t_{1}=6 \cdot \ 0.5=3 \ \text{km} \ \\ s_{2}=v_{2} \cdot \ t_{2}=30 \cdot \ 2.5=75 \ \text{km}$

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