Two trains

Through the bridge, long l = 240 m, the train passes through the constant speed at time t1 = 21 s. A train running along the traffic lights at the edge of the bridge passes the same speed at t2 = 9 s.

a) What speed v did the train go?
b) How long did a train driver cross the bridge take?
c) What is the L train length?
d) How long will it take for a train to overtake in the same direction with the same length but half the speed?
e) How long will it take for a train to overtake in the opposite direction with the same length but half the speed?

Final Answer:

v =  20 m/s
L =  180 m
t₃ =  12 s
t₄ =  36 s
t₅ =  12 s

Step-by-step explanation:

$$\begin{gathered} l=240\text{m} \\ {t}_1=21\text{s} \\ {t}_2=9\text{s} \\ L=9\cdot v \\ L+240=21\cdot v \\ L-9v=0 \\ L-21v=-240 \\ Row2-Row1\to Row2 \\ -12v=-240 \\ v=\frac{-240}{-12}=20 \\ L=0+9v=0+9\cdot 20=180 \\ L=180 \\ v=20=20\text{m/s} \end{gathered}$$

$L=180=180\text{m}$

$t_3=l/v=240/20=12\text{s}$

$t_4=\frac{2\cdot L}{v-v/2}=\frac{2\cdot 180}{20-20/2}=36\text{s}$

$t_5=\frac{2\cdot L}{v+v/2}=\frac{2\cdot 180}{20+20/2}=12\text{s}$

Try another example