Where and when

The truck left Kremnica at 11:00 h at a speed of 60km/h. At 12:30 h, the passenger car started at an average speed of 80km/h. How many kilometers from Kremnica will the passenger car reach truck, and when?

Result

s =  360 km
T = 17:00 hh:mm

Solution:

$s_{ 1 } = s_{ 2 } \ \\ v_{ 1 } = 60 \ km/h \ \\ v_{ 2 } = 80 \ km/h \ \\ \ \\ \ \\ v_{ 1 } \cdot \ (t-11.00) = v_{ 2 } \cdot \ (t-(12+30/60)) \ \\ \ \\ 60 \cdot \ (t-11.00) = 80 \cdot \ (t-(12+30/60)) \ \\ \ \\ 1200t = 20400 \ \\ \ \\ t = 17 \ \\ \ \\ s = v_{ 1 } \cdot \ (t-11.00) = 60 \cdot \ (17-11.00) = 360 = 360 \ \text{ km }$

$T = t = 17 = 17:00 \ \text{ hh:mm }$

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