The problem asks for the time it takes for a truck to cross a train moving in the same direction. We need to use the concept of relative speed.

Calculating Relative Speed

The truck's speed ($S_T$) is 112 km/hr and the train's speed ($S_{Tr}$) is 82 km/hr. Since they are moving in the same direction, the relative speed ($S_{rel}$) is the difference between their speeds:

$ S_{rel} = S_T - S_{Tr} $

$ S_{rel} = 112 \text{ km/hr} - 82 \text{ km/hr} = 30 \text{ km/hr} $

Converting Speed to Metres per Second

To find the time in seconds, we need to convert the relative speed from km/hr to m/s. The conversion factor is:

$ 1 \text{ km/hr} = \frac{5}{18} \text{ m/s} $

Therefore, the relative speed in m/s is:

$ S_{rel} = 30 \times \frac{5}{18} \text{ m/s} = \frac{150}{18} \text{ m/s} = \frac{25}{3} \text{ m/s} $

Determining Total Distance

The total distance ($D$) the truck must cover to completely cross the train is the sum of the truck's length ($L_T$) and the train's length ($L_{Tr}$).

Truck length ($L_T$) = 1600 metres

Train length ($L_{Tr}$) = 1500 metres

$ D = L_T + L_{Tr} $

$ D = 1600 \text{ m} + 1500 \text{ m} = 3100 \text{ m} $

Calculating Crossing Time

The time ($T$) taken to cross is calculated using the formula:

$ T = \frac{\text{Total Distance}}{\text{Relative Speed}} $

$ T = \frac{D}{S_{rel}} $

$ T = \frac{3100 \text{ m}}{\frac{25}{3} \text{ m/s}} $

$ T = 3100 \times \frac{3}{25} \text{ seconds} $

$ T = \frac{9300}{25} \text{ seconds} $

$ T = 372 \text{ seconds} $

Thus, it will take the truck 372 seconds to cross the train.