Question

A train travelling at 42 km/h passes a runner in 9 seconds running in same direction and took 5 seconds in the opposite direction. find the length of the train.

Answer 1

Same direction: Relative speed=  Difference in speed of train & man
Opposite direction: Relative speed = Add the respective speeds
Let the length of train be 'L' = distance
Speed of man = m km/hr
L/(42-m) = 9 = 9/3600 hrs
L = (42-m)*9/3600 ...(i)
L/(42+m) = 5/3600 hrs
L - (42+m)*5/3600...(ii)
Dist = L = same
Hence, equate (i) & (ii)
(42-m)*9/3600 = (42+m)*5/3600
42*9 - 9*m = 42*5 + 5*m
42*(9-5) = m*(5+9)
42*4 = m*14
m = 42*4/14 = 12
Speed of man = 12 km/hr
Substitute this 'm' in (i)
L = (42-m)* 9/3600 = (42-12)* 9/3600 = 30*9/3600 = 0.075 km = 75 m
Hence, length of train = 75 m
Hope it helps.

Answer 2

Answer:

75 m

Step-by-step explanation:

400L = 42 - x (i)

720L = 42 + x. (ii)

adding both

1120 L = 84

L = 84 x 1000

________

1120

= 75