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A train traveling 60% faster than a car. Both start from point A at the same time and reach point B, 160 km away at the same time. On the way, the train takes 20 minutes for stopping at the stations. What is the speed (in km/hr) of the train? 
  • a)
    144 
  • b)
    168 
  • c)
    198 
  • d)
    288 
Correct answer is option 'D'. Can you explain this answer?
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A train traveling 60% faster than a car. Both start from point A at th...
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A train traveling 60% faster than a car. Both start from point A at th...
Given:
Distance between point A and point B = 160 km
Time taken by both train and car to reach point B is equal
Train stops for 20 minutes on the way

Let's assume:
Speed of car = x km/hr
Speed of train = y km/hr

Calculation:
As per the question, the train is traveling 60% faster than the car
Hence, y = (100 + 60)x/100 = 1.6x

Let's calculate the time taken by the car to travel from point A to point B
Time = Distance/Speed
Time taken by the car = 160/x

Let's calculate the time taken by the train to travel from point A to point B
Time taken by the train = (160 - time taken for stopping)/Speed
Time taken for stopping = 20/60 = 1/3 hours
Time taken by the train = (160 - 1/3)/y

As per the question, time taken by both train and car to reach point B is equal
160/x = (160 - 1/3)/y

Substituting y = 1.6x in the above equation, we get
160/x = (160 - 1/3)/(1.6x)
160/x = 100/(16/3)x
160/x = 600/16
x = 10/3 km/hr

Speed of train = 1.6x = 1.6 × 10/3 = 16/3 × 1.6 = 64/3 km/hr

Converting km/hr to m/s
Speed of train = 64/3 × 5/18 = 80 m/s

Converting m/s to km/hr
Speed of train = 80 × 18/5 = 288 km/hr

Hence, the correct answer is option D, 288.
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A train traveling 60% faster than a car. Both start from point A at the same time and reach point B, 160 km away at the same time. On the way, the train takes 20 minutes for stopping at the stations. What is the speed (in km/hr) of the train?a)144b)168c)198d)288Correct answer is option 'D'. Can you explain this answer?
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