train is 14m/s distance is 12m? i really confused myself doing this lol
edit: lol no this is very wrong.. i shouldnt try doing two things at once
edit 2: solved now i have my full attention :P
20-v=DT(1) DT(1) is difference in time of the car going same way as the train
15+v=DT(2) DT(2) is difference in time of the car going different way as the train
DT2*12=S going at difference in time 2, for 12 seconds= passing the distance of train
DT1*72=S going at difference in time 1, for 72 seconds= passing the distance of train
(15+v)*12=S subsituting from the first set of eqs into the second gives these new equations
(20-v)*72=S
180+12v=S multiplying out the brackets gets you these simplifications
1440-72v=S
180+12v=1440-72v putting the two equations equal to each other and rearranging get you this
180-1440=-72v-12v
-1260=-84v
v=15m/s
so the trains going at 15m/s and the car going the same way as it at 20m/s... the car takes 5m/s out of the train for 72 seconds passing it, so the train is 72*5 which is 360m long.
checking, the train is going 15m/s and the car going the opposite way is going at 15m/s... so taking 30meters out of the train every second for 12 seconds. 30*12= 360m. prooved
