A train 2

A train 90 meters long is moving at speed 80 km/h overtakes a second train moving at 56 km/h in the same direction and passes completely in 25 1/2 seconds. Compute how long is the second train.

Final Answer:

b =  80 m

Step-by-step explanation:

$$\begin{gathered} a=90\text{m} \\ {v}_1=80\text{km/h}\to \text{m/s}=80:3.6\text{m/s}=22.22222\text{m/s} \\ {v}_2=56\text{km/h}\to \text{m/s}=56:3.6\text{m/s}=15.55556\text{m/s} \\ {t}_1=25\frac{1}{2}=25+\frac{1}{2}=\frac{25\cdot 2+1}{2}=\frac{50+1}{2}=\frac{51}{2}=25.5\text{s} \\ v=v_1-v_2=\frac{200}{9}-\frac{140}{9}=\frac{200-140}{9}=\frac{60}{9}=\frac{20}{3}\doteq 6.6667\text{m/s} \\ v=\frac{a+b}{t_1} \\ b=v\cdot t_1-a=\frac{20}{3}\cdot \frac{51}{2}-90\text{m}=80\text{m} \end{gathered}$$

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