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A motorist travels to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/hr. What is the average speed of the journey?
- a)35 km/hr
- b)37 km/hr
- c)37.5 km/hr
- d)40 km/hr
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A motorist travels to a place 150 km away at an average speed of 50 km...
The speeds of the motorist are 50 and 30 km/hr;
Average speed = Total Distance/Total Time = (150 + 150)/(150/50 + 150/30)
⇒ 300/(5 + 3) = 300/8
⇒ 37.5 km/hr
⇒ 300/(5 + 3) = 300/8
⇒ 37.5 km/hr
Most Upvoted Answer
A motorist travels to a place 150 km away at an average speed of 50 km...
Solution:
To find the average speed of the journey, we need to apply the formula:
Average speed = Total Distance / Total Time
Let us assume that the distance covered by the motorist in each direction is 'd'. Therefore, the total distance covered by the motorist is:
Total Distance = d + d = 2d
Time taken to cover the distance in the first direction:
Time taken = Distance / Speed = d / 50
Time taken to cover the distance in the opposite direction:
Time taken = Distance / Speed = d / 30
Total time taken for the journey:
Total Time = d/50 + d/30
= (3d + 5d) / 150
= 8d / 150
= 4d / 75
Average speed of the journey:
Average speed = Total Distance / Total Time
= 2d / (4d/75)
= 50 km/hr
Therefore, the average speed of the journey is 37.5 km/hr.
Final answer: Option C
To find the average speed of the journey, we need to apply the formula:
Average speed = Total Distance / Total Time
Let us assume that the distance covered by the motorist in each direction is 'd'. Therefore, the total distance covered by the motorist is:
Total Distance = d + d = 2d
Time taken to cover the distance in the first direction:
Time taken = Distance / Speed = d / 50
Time taken to cover the distance in the opposite direction:
Time taken = Distance / Speed = d / 30
Total time taken for the journey:
Total Time = d/50 + d/30
= (3d + 5d) / 150
= 8d / 150
= 4d / 75
Average speed of the journey:
Average speed = Total Distance / Total Time
= 2d / (4d/75)
= 50 km/hr
Therefore, the average speed of the journey is 37.5 km/hr.
Final answer: Option C
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A motorist travels to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/hr. What is the average speed of the journey?a)35 km/hrb)37 km/hrc)37.5 km/hrd)40 km/hrCorrect answer is option 'C'. Can you explain this answer?
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