Aidan and Bradwick are standing back to back next to a railroad track.
When the front of a train passes them, Aidan starts to walk in the opposite direction of the train, while Bradwick starts to walk in the same direction as the train. Each stops walking when the back of the train passes him.
If the two of them walk at the same speed, and Aidan walks exactly 30 feet, and Bradwick walks exactly 45 feet, how long is the train?
I was also thinking of an overriding method. Here is how to get the relative train speed from the ratio of distances walked... (a very similar simplification to the one given by Brian.)
There is a proportional relationship between walker time and walker distance. There is a reciprocal relation between velocity and time for all three objects, and time is added or subtracted by the train crossing time for each walker to give a distance-walked ratio of 2/3. So, if f is the fraction of walker speed to train speed,
[v (1-f)]/[v (1+f)] = (1-f)/(1+f) = 2/3,
f=1/5
Knowing 1/5 gives the train length.
Edited on November 9, 2023, 1:31 pm
or...
