two trains, each 100m long, moving in opposite directions, cross each other in 8 seconds. if one train is moving twice as fast as the other, then find the speed of the faster train in kilometers
Question
two trains, each 100m long, moving in opposite directions, cross each other in 8 seconds. if one train is moving twice as fast as the other, then find the speed of the faster train in kilometers
Solution
Sure, let's solve this step by step:
Step 1: Understand the problem Two trains of equal length are moving in opposite directions and cross each other in 8 seconds. The speed of one train is twice that of the other. We need to find the speed of the faster train.
Step 2: Define the variables Let's denote the speed of the slower train as 'x' m/s. Therefore, the speed of the faster train would be '2x' m/s.
Step 3: Set up the equation When two objects move in opposite directions, their relative speed is the sum of their speeds. So, the relative speed of the two trains is x + 2x = 3x m/s.
Step 4: Use the given information We know that the total length of the two trains is 100m + 100m = 200m. And they cross each other in 8 seconds. So, using the formula speed = distance/time, we can write the equation as 3x = 200m / 8s.
Step 5: Solve the equation Solving the equation 3x = 200m / 8s gives x = 25 m/s. This is the speed of the slower train.
Step 6: Find the speed of the faster train The speed of the faster train is 2x = 2*25 m/s = 50 m/s.
Step 7: Convert the speed to km/h We know that 1 m/s = 3.6 km/h. So, the speed of the faster train in km/h is 50 m/s * 3.6 km/h = 180 km/h.
So, the speed of the faster train is 180 km/h.
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