Two locomotives approach each other on parallel tracks. Each has and average spend of 150 km/h with respect to the ground. If they are initialy 8.5 km apart, how Long will it be before they reach each other?
To find out how long it will take for the two locomotives to meet, we can use the formula:
Time = Distance / Speed
Let's calculate the time it takes for one of the locomotives to travel the distance of 8.5 km:
Time = 8.5 km / 150 km/h
= 0.0567 hours
Since both locomotives are approaching each other, the time it will take for them to meet is the same for both. Therefore, the locomotives will reach each other after approximately 0.0567 hours or 3.4 minutes.
To determine how long it will take for the two locomotives to reach each other, you need to calculate the time it takes for them to cover the initial distance of 8.5 km.
Both locomotives have an average speed of 150 km/h with respect to the ground. Since they are moving towards each other, their speeds will be additive.
The total relative speed of the locomotives can be calculated by adding their individual speeds: 150 km/h + 150 km/h = 300 km/h.
To find the time it takes to cover the initial distance, divide the initial distance by the relative speed:
Time = Distance / Speed
Time = 8.5 km / 300 km/h
To ensure consistent units, convert the distance to meters and the speed to meters per hour:
Time = (8.5 km * 1000) / (300 km/h * 1000 m/km)
Time = (8,500 m) / (300,000 m/h)
Simplifying the expression:
Time = 0.02833 hours
To convert this time to minutes, multiply by 60:
Time = 0.02833 hours * 60 minutes/hour
Time ≈ 1.70 minutes
Therefore, it will take approximately 1.70 minutes for the two locomotives to reach each other.