Multiple choice

A motorist covers a distance of $39$ km in $45$ minutes by moving at a speed of $x$ kmph for the first $15$ minutes, then moving at double the speed for the next $20$ minutes, then again moving at his original speed for the rest of the journey, then $x$ in kmph is equal to:

  1. $31.2$
  2. $36$
  3. $40$
  4. $52$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total distance = 39 km. Time = 45 min. 15 min at x, 20 min at 2x, 10 min at x. Distance = (x * 15/60) + (2x * 20/60) + (x * 10/60) = 39. (15x + 40x + 10x) / 60 = 39 => 65x = 39 * 60 = 2340 => x = 2340 / 65 = 36.

AI explanation

Using the formula Distance = Speed * Time, we convert the time intervals to hours: 15 minutes is 1/4 hr, 20 minutes is 1/3 hr, and 10 minutes is 1/6 hr. The total distance is the sum of the segments: (x * 1/4) + (2x * 1/3) + (x * 1/6) = 39. Finding a common denominator of 12 gives (3x + 8x + 2x) / 12 = 39, which simplifies to 13x / 12 = 39. Solving for x yields x = 36. The result is 36.

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