Multiple choice

A person travelled the distance of 220 km from point A to B at an average speed of 66 km/hr. The person travelled first 75 km at an average speed of 55 km/hr. For the rest of the distance, he covered some distance at 75 km/hr and remaining distance at 65 km/hr. Find the distance (in km rounded off to the nearest integer) which was travelled at a speed of 65 km/hr.

  1. 15

  2. 16

  3. 17

  4. 18
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total distance = 220 km. Average speed = 66 km/hr. Total time = 220/66 = 10/3 hours. First 75 km at 55 km/hr = 75/55 = 15/11 hours. Remaining distance = 220 - 75 = 145 km. Remaining time = 10/3 - 15/11 = (110 - 45) / 33 = 65/33 hours. Let d be distance at 65 km/hr, then (145-d) is at 75 km/hr. Time = d/65 + (145-d)/75 = 65/33. Solving: 15d + 13(145-d) = (65/33) * 975. 2d + 1885 = 1920.3. 2d = 35.3. d = 17.65. Rounded = 18.

AI explanation

The total time taken for the 220 km journey at 66 km/hr is 10 divided by 3 hours. The time for the first 75 km at 55 km/hr is 15 divided by 11 hours, leaving 65 divided by 33 hours for the remaining 145 km. Letting y be the distance travelled at 65 km/hr, the equation is y divided by 75 plus (145 minus y) divided by 65 equals 65 divided by 33. Solving this equation gives y approximately equal to 18 km.

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