Train X can travel 50% faster than a car Y. Both start from New Delhi at the same time and reach Meerut which is 75 kms away from New Delhi at the same time. However, the train lost about 12.5 minutes while stopping at the stations. The speed of the car Y is:
Question
Train X can travel 50% faster than a car Y. Both start from New Delhi at the same time and reach Meerut which is 75 kms away from New Delhi at the same time. However, the train lost about 12.5 minutes while stopping at the stations. The speed of the car Y is:
Solution
To solve this problem, we need to first understand that the time taken by both the train and the car to reach Meerut is the same, except for the fact that the train lost 12.5 minutes stopping at stations.
Step 1: Convert the lost time to hours, since speed is usually measured in km/h. 12.5 minutes = 12.5/60 = 0.20833 hours
Step 2: Since the train and the car started at the same time and the train was delayed by 0.20833 hours, the time taken by the car to reach Meerut is the total time taken by the train minus the time the train lost.
Let's denote the time taken by the car as T (in hours). So, the time taken by the train to travel is T + 0.20833 hours.
Step 3: We know that Speed = Distance/Time. We can use this formula to express the speed of the train in terms of T. So, the speed of the train = 75/(T + 0.20833)
Step 4: The problem states that the train travels 50% faster than the car. This means that the speed of the train is 1.5 times the speed of the car.
So, 1.5 * (Speed of Car) = Speed of Train => 1.5 * (75/T) = 75/(T + 0.20833)
Step 5: Solve this equation for T. After solving, you get T = 0.83333 hours.
Step 6: Now, substitute T = 0.83333 hours into the speed formula to get the speed of the car. Speed of Car = 75/T = 75/0.83333 = 90 km/h
So, the speed of car Y is 90 km/h.
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