Multiple choice

An engineer travels 600 km to his home, partly by train and partly by car. He takes 8 hours if he travels 120 km by train and the rest by car. He takes 20 minutes longer if he travels 200 km by train and the rest by car. Find the speeds of the train and the car.

  1. 60 km/hr; 80 km/hr

  2. 30 km/hr; 40 km/hr

  3. 40 km/hr; 20 km/hr

  4. 20 km/hr; 40 km/hr

  5. 60 km/hr; 60 km/hr
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A Correct answer
Explanation

Let train speed be T, car speed be C. 120/T + 480/C = 8. 200/T + 400/C = 8 + 1/3 = 25/3. Solving this system: 1/T = 1/60, 1/C = 1/80. T = 60, C = 80.

AI explanation

Let the speed of the train be x km/hr and the speed of the car be y km/hr. Using the given conditions, 120 divided by x plus 480 divided by y equals 8, and 200 divided by x plus 400 divided by y equals 25 over 3. By expressing 1 over x and 1 over y as variables, these equations simplify to a system yielding 1 over x as 1 over 60 and 1 over y as 1 over 80. Solving for the speeds gives the train's speed as 60 km/hr and the car's speed as 80 km/hr.

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