A train can travel 50% faster than car. Both start from point A at the same time and reach point B , 100 km away from point A at the same time. On the way, however , the train, lost about 12.5 minutes while stopping at the stations . What is the speed of the car?
Question
A train can travel 50% faster than car. Both start from point A at the same time and reach point B , 100 km away from point A at the same time. On the way, however , the train, lost about 12.5 minutes while stopping at the stations . What is the speed of the car?
Solution
Let's solve this step by step:
Step 1: Let's assume the speed of the car is x km/hr. Since the train is 50% faster, the speed of the train is 1.5x km/hr.
Step 2: The time taken by both the car and the train to reach point B from point A is the same. So, we can say that the time taken by the car to travel 100 km is equal to the time taken by the train to travel the same distance plus the time the train lost stopping at stations.
Step 3: We know that time = distance/speed. So, we can set up the following equation: 100/x = 100/1.5x + 12.5/60.
Step 4: Simplify the equation to: 2/3x = 1/x + 12.5/60.
Step 5: Solve for x: 2/3x - 1/x = 12.5/60, which simplifies to: 2/3x^2 - 1 = 12.5/60.
Step 6: Solve the quadratic equation to find the value of x. The solution to this equation gives x ≈ 60 km/hr.
So, the speed of the car is approximately 60 km/hr.
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