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:*100 kmph110 kmph120 kmph130 kmph
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:*100 kmph110 kmph120 kmph130 kmph
Solution
Let's solve this step by step:
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Let's assume the speed of the car is x km/hr. Since the train travels 50% faster, the speed of the train is 1.5x km/hr.
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The distance from point A to point B is 75 km. The time taken by both the car and the train to travel this distance is the same, even though the train lost 12.5 minutes stopping at stations.
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We can express the time taken to travel as the distance divided by the speed. So, the time taken by the car is 75/x hours and the time taken by the train is 75/(1.5x) hours.
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However, the train lost 12.5 minutes, which is 12.5/60 = 0.20833 hours. So, the actual time taken by the train is 75/(1.5x) + 0.20833 hours.
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Since the time taken by the car and the train is the same, we can set these two expressions equal to each other and solve for x:
75/x = 75/(1.5x) + 0.20833
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To make the equation easier to solve, we can multiply every term by x and by 1.5x:
112.5 = 75 + 0.3125x
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Subtract 75 from both sides:
37.5 = 0.3125x
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Divide both sides by 0.3125:
x = 120
So, the speed of the car is 120 km/hr.
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