Multiple choice

A man travels $370$km partly by train and partly by car. If he covers $250$km by train and the rest by car, it takes him $4$ hours. But, if he travels $130$ km by train and the rest by car, he takes $18$ minutes longer. Find the speed of the train and car respectively.

  1. $80$ km/hr, $100$ km/hr
  2. $98$ km/hr, $100$ km/hr
  3. $100$ km/hr, $98$ km/hr
  4. $100$ km/hr, $80$ km/hr
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D Correct answer
Explanation

Let train speed be x and car speed be y. We have 250/x + 120/y = 4 and 130/x + 240/y = 4.3. Solving this system of equations yields x=100 and y=80.

AI explanation

Let the speed of the train be x km/hr and the speed of the car be y km/hr. From the first condition, 250 divided by x plus 120 divided by y equals 4, and from the second condition, 130 divided by x plus 240 divided by y equals 4.3, because 18 minutes is 0.3 hours. Solving these two equations gives x equals 100 and y equals 80, which means the respective speeds are 100 km/hr and 80 km/hr.

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