Multiple choice

A runner participates in a marathon and covers one-fourth of the total distance at a speed of 8 km/hr. Out of the total time taken to cover the remaining distance, the runner runs at a speed of 8 km/hr for one-third of the time and at a speed of 6 km/hr for the remaining time. What is the average speed of the runner?

  1. 6.34 km/hr

  2. 6.96 km/hr

  3. 7.56 km/hr

  4. 7.95 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total distance be 12 km. 1/4 (3 km) at 8 km/hr takes 3/8 hours. Remaining 9 km: let total time be T. 1/3 of T at 8 km/hr and 2/3 of T at 6 km/hr. Distance = 8*(T/3) + 6*(2T/3) = 9. 8T/3 + 4T = 9, 20T/3 = 9, T = 27/20 = 1.35 hours. Total time = 0.375 + 1.35 = 1.725 hours. Average speed = 12 / 1.725 = 6.956 km/hr.

AI explanation

Let the total distance be 96 km, so the first part is 24 km and the remaining part is 72 km. The time taken for the first part is 24 divided by 8, which is 3 hours. Let the time taken for the remaining part be 3t hours, meaning 2t hours are spent at 8 km/hr and t hours are spent at 6 km/hr. The distance covered in the remaining part is (8 multiplied by 2t) plus (6 multiplied by t), which equals 22t; setting this equal to 72 km gives t = 72/22. The total time is 3 plus 3t, which is 3 plus 216/22 equals 246/22 hours. The average speed is total distance 96 km divided by total time (246/22) hours, which equals 6.96 km/hr.

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