Multiple choice

Directions : Type in your answer in the input box provided below the question. Rahul covered a certain distance in four hours, covering a part of the distance by car, at a speed of 60 km/hr, and the rest of the distance by bike, at a speed of 45 km/hr. Had he interchanged the two modes of transport, it would have taken him 10 minutes more to cover the entire distance. Find the total distance (in km) covered by him. [quizky-text]

  1. 210

  2. 1

  3. 2 : 5

  4. 5 : 8
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A Correct answer
Explanation

Let d1 be car distance, d2 be bike distance. d1/60 + d2/45 = 4. d2/60 + d1/45 = 4 + 10/60 = 25/6. Solving this system: d1+d2 = 210 km.

AI explanation

Let the distance traveled by car be x and the distance traveled by bike be y, so the total time of 4 hours gives the equation x divided by 60 plus y divided by 45 equals 4. When the modes are interchanged, the 10 extra minutes is one-sixth of an hour, giving the equation y divided by 60 plus x divided by 45 equals 25 divided by 6. Multiplying the first equation by 180 gives 3x plus 4y equals 720, and multiplying the second equation by 180 gives 4x plus 3y equals 750, so solving the system yields x equals 120 and y equals 90, making the total distance 210 km.

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