Multiple choice

A man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But if he travels 200 km by train and the rest by car, he takes half an hour more. Find the speed of the train and the car.

  1. 100 km/hr and 80 km/hr

  2. 90 km/hr and 80 km/hr

  3. 200 km/hr and 80 km/hr

  4. 40 km/hr and 50 km/hr

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let T be train speed and C be car speed. 400/T + 200/C = 6.5 and 200/T + 400/C = 7. Solving this system: 1/T = 1/100 and 1/C = 1/80. Thus, T = 100 km/hr and C = 80 km/hr.

AI explanation

Let the speed of the train be x and the speed of the car be y; the two conditions give the equations 400/x plus 200/y equals 6.5 and 200/x plus 400/y equals 7. Multiplying the first equation by two and subtracting the second eliminates y, resulting in 600/x equaling 6, so x is 100 km/hr. Substituting x into the first equation gives 4 plus 200/y equals 6.5, which means y is 80 km/hr.

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