Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
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.
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.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.