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:

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

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