Motion

From two different locations distant 232 km started against car and bus. The car started at 5:20 with average speed 64 km/h. Bus started at 7:30 with average speed 80 km/h.

When they meet?
How many kilometers went the bus?

Result

x (hh:mm) = 8:09 Wrong answer
s2 =  51.9 km

Solution:

 Δt=(7−5)+160⋅(30−20)=2.17 h  s1+s2=232 v1(t+Δt)+v2t=232  t=232−64⋅Δt64+80=0.65 h x=5+160⋅20+t+Δt=8.153 x=8:09 \ \\ \Delta t = (7-5)+\dfrac{1}{60}\cdot (30-20) = 2.17 \ h \ \\ \ \\ s_1 + s_2 = 232 \ \\ v_1(t+\Delta t) + v_2 t = 232 \ \\ \ \\ t = \dfrac{ 232-64 \cdot \Delta t} { 64+80} = 0.65 \ h \ \\ x = 5 + \dfrac{1}{60}\cdot 20 + t + \Delta t = 8.153 \ \\ x = 8:09
s2=v2t=80⋅0.65=51.9 kms_2 = v_2 t = 80 \cdot 0.65 = 51.9 \ \text{km}

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