# Two trains

The train runs at speed v1 = 72 km/h. The passenger, sitting in the train, observed that a train long l = 75m in 3 s passed on the other track in the opposite direction. Calculate the speed of this train.

Result

v2 =  18 km/h

#### Solution:

$v_{1}=72 \ km/h \rightarrow m/s=72 / 3.6 \ m/s=20 \ m/s \ \\ l=75 \ \text{m} \ \\ t=3 \ \text{s} \ \\ \ \\ t=\dfrac{ l }{ v_{1}+v_{2} } \ \\ \ \\ v_{1} \cdot \ t+v_{2} \cdot \ t=l \ \\ \ \\ v_{22}=\dfrac{ l-v_{1} \cdot \ t }{ t }=\dfrac{ 75-20 \cdot \ 3 }{ 3 }=5 \ \text{m/s} \ \\ \ \\ v_{2}=v_{22} \rightarrow km/h=v_{22} \cdot \ 3.6 \ km/h=5 \cdot \ 3.6 \ km/h=18 \ km/h=18 \ \text{km/h}$

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