Three trains A, B and C, are travelling along 3 parallel tracks. Each train is the same length as the others. A is travelling in the same direction as B and takes 24 seconds to overtake it. C is travelling in the opposite direction but is travelling at the same speed as A and it takes 8 seconds to pass B. How much faster than B is C travelling? And how long did it take A and C to pass each other?
Thanks for any help.
Give the trains an arbitrary length of, say, 240 meters each. Since train A overtatakes train B, it means A is moving faster than B. Or, A - B =240 meters divided by 24 seconds =10 meters per second.
Since train C is also moving faster, which is the same speed as A, than train B, it appears to be moving at C + B meters per second. But, since A and C have the same speed, then A + B =meters per second.
Since it takes C 8 seconds to pass B, then A + B =240 meters divided by 8 seconds =30 meters per second.
Since we know from the above A - B =10 meters per second, it follows from both equations that:
A=20 meters per second and B = 10 meters per second. And, since A and C are travelling at the same speed, then A = C = 20 meters per second, which twice as fast as train B. Moreover, If A and C are travelling at the same speed, or 20 meters per second, their combined speed is 20 + 20 = 40 meters per second, when they pass each other.
Finally, since the A and C trains are 240 meters long, it therefore takes: 240 / 40 = 6 seconds to pass each other.
MODERATORS:Please verify my reasoning!!.
