Time taken by a train 70 metres long to cross a bridge of length 105 metres with a speed of 75 kmph is

Given:

Length of train (L_train) = 70 metres

Length of bridge (L_bridge) = 105 metres

Speed of train (S) = 75 kmph

Formula used:

Total Distance (D) = Length of train + Length of bridge

Time (T) = \(\dfrac{\text{Total Distance}}{\text{Speed}}\)

Calculations:

⇒ S = 75 kmph = 75 × \(\dfrac{5}{18}\) m/s

⇒ S = \(\dfrac{25 \times 5}{6}\) m/s (dividing 75 and 18 by 3)

⇒ S = \(\dfrac{125}{6}\) m/s

⇒ Total Distance = L_train + L_bridge

⇒ Total Distance = 70 m + 105 m = 175 m

⇒ Time = \(\dfrac{\text{Total Distance}}{\text{Speed}}\)

⇒ Time = \(\dfrac{175}{\frac{125}{6}}\)

⇒ Time = \(\dfrac{175 \times 6}{125}\)

⇒ Time = \(\dfrac{7 \times 6}{5}\)

⇒ Time = \(\dfrac{42}{5}\) seconds = \(8 \frac{2}{5}\) sec

∴ The time taken by the train to cross the bridge is \(8 \frac{2}{5}\) seconds.