Multiple choice

A person travels two parts of the total distance in the ratio 2 : 1 with constant speed of $\displaystyle { 30 km }\ { h }^{ -1 }\ and \ { 40 km }\ { h }^{ -1 }$ respectively. The average speed of the journey is ____ $\displaystyle { km } { h }^{ -1 }$

  1. $13.5$ 
  2. $62.2$ 
  3. $42.5$ 
  4. $32.7$ 
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Average speed = Total Distance / Total Time. Let total distance be 3D. Part 1 = 2D, time = 2D/30. Part 2 = D, time = D/40. Total time = 2D/30 + D/40 = 8D/120 + 3D/120 = 11D/120. Average speed = 3D / (11D/120) = 360/11 = 32.72.

AI explanation

Let the two parts of the distance be 2d and d, making the total distance equal to 3d. The total time taken for the journey is 2d divided by 30 plus d divided by 40, which equals 11d/120. The average speed is the total distance divided by the total time, so 3d divided by 11d/120 gives an average speed of 360/11 km/hr, which is approximately 32.7 km/hr.

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