# Steamship

Between the two ports on the river is going steamship. The journey there and back takes 8:42. Downstream steamship traveling at 20 km/h, upstream 9 km/h.

What is the distance between the ports?

Correct result:

x =  54 km

#### Solution:

$\ \\ x = s_1 = s_2 \ \\ s_1 = v_1 t_1 \ \\ s_2 = v_2 t_2 \ \\ t_1 + t_2 = 8.7 h \ \\ v_1 t_1 = v_2 (8.7-t_1) \ \\ t_1 = \dfrac{ v_2 \cdot 8.7 }{ v_1 + v_2} = 2.7 \ h \ \\ t_2 = 8.7 - t_1 = 6 \ h \ \\ \ \\ x = v_1 t_1 = \dfrac{ 20 \cdot 9 }{ 20+9} \cdot 8.7 = 54 \ \text{km}$

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