Final answer:
The two trains will meet in 0.0159 hours. The position equations for Train A and Train B are x = 90t and y = 2.71 - 80t, respectively. The trains will be at the same position after approximately 0.016 hours.
Step-by-step explanation:
To find the time it will take for the two trains to meet, we can use the formula:
Time = Distance / Relative Speed
The distance between the two trains is initially given as 2.71 km. The relative speed is the sum of the speeds of the two trains, which is 90 km/hr (Train A) + 80 km/hr (Train B) = 170 km/hr.
Substituting the values into the formula, we get:
Time = 2.71 km / 170 km/hr = 0.0159 hours
To write the position equations for each train, we can assume that Train A is at position x and Train B is at position y. The positions can be written as:
Position of Train A: x = 90t
Position of Train B: y = 2.71 - 80t
To find the exact time when the two trains are at the same position, we can set the positions equal to each other:
90t = 2.71 - 80t
Solving for t, we get:
170t = 2.71
t = 2.71 / 170 = 0.016 hours
At this exact time, the positions of both trains will be the same.
To find the position of Train A when it meets Train B, we can substitute the value of t into the position equation of Train A:
x = 90 * 0.016 = 1.44 km
Finally, to find how far Train B has traveled in this time, we can substitute the value of t into the position equation of Train B:
y = 2.71 - 80 * 0.016 = 1.37 km