# Moving

Vojta left the house at three o'clockat 4 km/h. After half hour later went from the same place Filip by bicycle at speed 18 km/h.

How long take Tilip to catch up Vojta and how far from the house?

Result

t =  11.5 min
s =  3.5 km

#### Solution:

$v_1 = 5 km/h \ \\ v_2 = 18 km/h \ \\ \ \\ s_1 = s_2 = s \ \\ v_1(t+30) = v_2 t \ \\ 5 t + 30 \cdot 5 = 18 t \ \\ \ \\ t = 11.5 \ \text{min}$
$s = s_1 = v_1 (t + 30 \ min) = 3.5 \ \text{km}$

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