Truck

In 7 hours, we started from the town Krnov truck at a speed of 40 km/h. Passenger cars started against it in 8 hours 30 minutes from the city of Jihlava at a speed of 70 km/h. The distance between these two cities is 225 km. At what time and distance do these two cars meet from Krnov? Sketch the situation.

Result

t = 10:00 h
s₁ =  120 km

Step-by-step explanation:

$v_{1} = 40 \ \text{km/h} \ \\ v_{2} = 70 \ \text{km/h} \ \\ t_{1} = 7:0 = 7\ hr\ 0\ min\ = 7 + \dfrac{ 0 }{ 60 } = 7 \ hr = 7 \ \\ t_{2} = 8:30 = 8\ hr\ 30\ min\ = 8 + \dfrac{ 30 }{ 60 } = 8.5 \ hr = 8.5 \ \\ s = 225 \ \text{km} \ \\ Δt = t_{2}-t_{1} = 8.5-7 = \dfrac{ 3 }{ 2 } = 1.5 \ \text{h} \ \\ \ \\ s = v_{1} \cdot \ x + v_{2} \cdot \ (x-Δt) \ \\ 225 = 40 \cdot \ x + 70 \cdot \ (x-1.5) \ \\ \ \\ 110x = 330 \ \\ \ \\ x = \dfrac{ 330 }{ 110 } = 3 \ \\ \ \\ x = 3 \ \\ \ \\ t = t_{1}+x = 7+3 = 10 = 10:00 \ \text{h}$

$s_1=v_1\cdot x=40\cdot 3=120\text{km}$

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