To find the time it takes for a train to cross a bridge, we need to follow a series of steps. Here’s a detailed, step-by-step solution:
1. Determine the total distance the train needs to travel to completely cross the bridge:
- The length of the train is [tex]\(340\)[/tex] meters.
- The length of the bridge is [tex]\(160\)[/tex] meters.
- Therefore, the total distance to travel is the sum of these lengths:
[tex]\[
\text{Total distance} = 340 \, \text{meters} + 160 \, \text{meters} = 500 \, \text{meters}
\][/tex]
2. Convert the speed of the train from kilometers per hour to meters per second:
- The given speed is [tex]\(45\)[/tex] kilometers per hour.
- There are [tex]\(1000\)[/tex] meters in a kilometer and [tex]\(3600\)[/tex] seconds in an hour.
- Therefore, to convert kilometers per hour to meters per second:
[tex]\[
\text{Speed in meters per second} = 45 \, \text{km/hr} \times \frac{1000 \, \text{m}}{3600 \, \text{s}}
\][/tex]
- Simplify this conversion:
[tex]\[
\text{Speed in meters per second} = 45 \times \frac{1000}{3600} = 45 \times \frac{5}{18} = 12.5 \, \text{m/s}
\][/tex]
3. Calculate the time required to travel the total distance at the given speed:
- We know the formula for time when distance and speed are given:
[tex]\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\][/tex]
- Substituting the values we have:
[tex]\[
\text{Time to cross} = \frac{500 \, \text{meters}}{12.5 \, \text{meters/second}}
\][/tex]
- Perform the division:
[tex]\[
\text{Time to cross} = 40 \, \text{seconds}
\][/tex]
4. Conclusion:
- Therefore, the train will take [tex]\(40\)[/tex] seconds to cross the [tex]\(160\)[/tex] meter long bridge.
