Multiple choice

The distance travelled by a person in 9 hours is 610 km. Some of the portion of his journey is travelled in a bus running at 40 km/hr and remaining in a train running at 90 km/hr. How much distance has the person travelled by bus?

  1. 160 km

  2. 210 km

  3. 150 km

  4. 200 km

  5. 110 km
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A Correct answer
Explanation

Let x be the distance by bus and (610-x) by train. Time = x/40 + (610-x)/90 = 9. Multiply by 360: 9x + 4(610-x) = 3240. 9x + 2440 - 4x = 3240. 5x = 800. x = 160 km.

AI explanation

Let the time spent on the bus be t hours, making the time spent on the train 9 minus t hours. Using the formula Distance equals Speed multiplied by Time, the sum of the distances equals 610 km, so 40 multiplied by t plus 90 multiplied by 9 minus t equals 610. Expanding and simplifying this equation gives 810 minus 50 times t equals 610, which means t equals 4 hours. Multiplying the 4 hours on the bus by its speed of 40 km/hr gives a bus distance of 160 km.

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