A train of length of $5km$ is running at a speed of $\frac{2.5km}{h}$ with some uniform stoppages every hour. For how long did the train stop in each hour if the train crossed a platform of half its length in $4$ hours and $20$ minutes?
(a) 20 min
(b) 30 min
(c) 35 min
(d) 40 min
How to solve this problem? Any help is appreciated.
Velocity of the train = $\frac{2.5km}{h}$
Length of the train = $l = 5km$
Distance traveled = $l + \frac{l}{2} = 7.5km$
Time spent to travel that distance = $\frac{7.5}{2.5} = 3$hours
3 hours = 3 stops that costs it a delay of 1 hours and 20 minutes, hence every stop costs it a delay of $\frac{80m}{3} = 26.67$ minutes on each stop.
But any letter contains that option, so I assumed that it made a stop before it starts to move, therefore, $4$ stops costs it a delay of $80$ minutes, and each stop was $20$ minutes long!