Multiple choice

Directions: Answer the questions independently of each other. Two people start their journies from point A to B with an initial speed of 10 km/hr. The first person then increases his speed by 10 km/hr for every successive 10% of the distance till B, whereas the second person increases his speed by 10 km/hr for every successive 10% of the time of his journey till he reaches B. Who reaches B first?

  1. first person

  2. both reach at the same time

  3. second person

  4. cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The first person increases speed based on distance, while the second person increases speed based on time. Since the second person increases speed earlier in the journey (time-based), they maintain a higher average speed for a longer duration, reaching B first.

AI explanation

Assume the total distance is 10 km, so each 10 percent segment is 1 km, and let the base speed be 10 km/hr. The first person travels at 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 km/hr, taking a total time of 1/10 + 1/20 + 1/30 + 1/40 + 1/50 + 1/60 + 1/70 + 1/80 + 1/90 + 1/100 hours, which equals approximately 0.292 hours. The second person travels for equal time intervals at increasing speeds, and since the first person's average speed across all intervals is heavily skewed toward the slower initial speeds while the second person's average speed is simply the overall average, the second person finishes the journey much faster.

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