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A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is

Question

A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is

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Solution

Let's solve this step by 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 would be 1.5x km/hr.

  2. The time taken by the car to cover the 75 km distance is the same as the time taken by the train (even with the 12.5 minutes delay). So, we can set up the following equation using the formula time = distance/speed:

    For the car: 75/x = time taken by the car

    For the train: 75/1.5x + 12.5/60 = time taken by the train

  3. Since the times are equal, we can set the two equations equal to each other and solve for x:

    75/x = 75/1.5x + 12.5/60

    Simplifying this equation gives:

    1/x = 1/1.5x + 12.5/4500

    Multiply through by 4500x to clear the fractions:

    4500 = 3000 + 12.5x

    Subtract 3000 from both sides:

    1500 = 12.5x

    Divide by 12.5:

    x = 120 km/hr

So, the speed of the car is 120 km/hr.

This problem has been solved

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