A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
(Train)

dsuc.created: 2 years ago | dsuc.updated: 1 year ago

dsuc.updated: 1 year ago

Let, the length of train is x meter and the velocity of the train is v km/hr.

According to first condition, $\frac{x}{(v - 4.5) \frac{5}{18}} = 8.4 . . . . . . . . . . . . . (i) [∵ \frac{D i s \tan c e}{V e l o c i t y} = T i m e]$

According to second condition, $\frac{x}{(v - 5.4) \frac{5}{18}} = 8.5 . . . . . . . . . . . . (i i)$

From equation (i) $\frac{x}{(v - 4.5) \frac{5}{18}} = 8.4$

$= x = (v - 4.5) \times \frac{5}{18} \times 8.4 = x = (v - 4.5) \times \frac{42}{18} = x = \frac{7 (v - 4.5)}{3} = 3 x = 7 v - 314.5 = 18 x = 42 v - 182 . . . . . . . . . . . . (i i i) F r o m E q u a t i o n (i i) \frac{x}{(v - 5.4) \frac{5}{18}} = 8.5 = x = 8.5 \times \frac{5}{18} (v - 5.4) = 18 x = 42.5 v - 229.5 . . . . . . . . . . (i v) S u b t r a c t i n g e q u a t i o n (i i i) f r o m e q u a t i o n (i v) \frac{18 x = 42.5 v - 229.5 18 x = 42 v - 189}{0 = 0.5 v - 40.5} = 0.5 v = 40.5 ∴ v = \frac{40.5}{0.5} = 81 ∴ T h e v e l o c i t y o f t h e t r a i n i s 81 k m p h . (a n s w e r)$