Final answer:
To find the time it takes for Train A and Train B to meet, we sum their speeds and divide the initial distance by this sum. It takes 0.0159 hours or approximately 0.95 minutes for the trains to meet. At this time, Train A is 1.431 km from its starting point, and Train B has traveled 1.272 km.
Step-by-step explanation:
To solve this question, we'll need to set up and solve some basic kinematic equations to find out when and where the trains will meet. Both trains approach each other on parallel tracks, so their speeds add up when determining how quickly the distance between them closes.
Train A Position Equation
Let xA represent Train A's position and vA represent its speed.
xA = vA * t
xA = 90 km/h * t
Train B Position Equation
Let xB represent Train B's starting position (2.71 km ahead of Train A) and vB represent its speed.
xB = 2.71 km - vB * t
xB = 2.71 km - 80 km/h * t
Determining Time and Positions When Trains Meet
To find out when they meet, we equate xA to xB.
90 km/h * t = 2.71 km - 80 km/h * t
170 km/h * t = 2.71 km
t = 2.71 km / 170 km/h
t = 0.0159 hours, or approximately 0.95 minutes
Position of Train A
Using Train A's position equation:
xA = 90 km/h * 0.0159 hours
xA = 1.431 km
Distance Traveled by Train B
Train B's distance can be calculated using the time it took for them to meet:
Distance traveled by Train B = 80 km/h * 0.0159 hours
Distance traveled by Train B = 1.272 km