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?
L=180 ft
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v_t = v train, v_w=v walkers, L = length train, t_a = time A walks
(v_w t_b)/(v_w t_a) = t_b/t_a = 45/30 = 3/2
t_a = L/(v_t+v_w) as w.r.t. the train's frame
t_b = L/(v_t-v_w)
t_b/t_a = (v_t + v_w)/(v_t - v_w)=3/2
3 v_t + 3 v_w = 2 v_t - 2 v_w
v_t = 5 v_w; (train's going 5 x the speed of walkers)
in time t_b, B walks 45, train goes L+45
45 + L = v_t t_b = 5 v_w t_b = 5 x 45
L=180
Edited on November 9, 2023, 10:26 am
soln
