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An automobile travels from city A to city B and returns to city A by the same route. The speed of the vehicle during the onward and return journeys were constant at 60 km/h and 90 km/h, respectively. What is the average speed in km/h for the entire journey?
- a)72
- b)73
- c)74
- d)75
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
An automobile travels from city A to city B and returns to city A by t...
Understanding Average Speed
To find the average speed for the entire journey, we use the formula:
Average Speed = Total Distance / Total Time
Step 1: Define the Distance
- Let the distance from city A to city B be "d" kilometers.
Step 2: Calculate Total Distance
- The total distance for the round trip is:
- Total Distance = d (to B) + d (return to A) = 2d
Step 3: Calculate Time for Each Leg of the Journey
- For the onward journey (A to B) at 60 km/h:
- Time = Distance / Speed = d / 60 hours
- For the return journey (B to A) at 90 km/h:
- Time = Distance / Speed = d / 90 hours
Step 4: Calculate Total Time
- Total Time = Time (to B) + Time (to A)
- Total Time = (d / 60) + (d / 90)
- To add these fractions, find a common denominator (which is 180):
- Total Time = (3d / 180) + (2d / 180) = (5d / 180) = (d / 36) hours
Step 5: Calculate Average Speed
- Now, substitute Total Distance and Total Time into the average speed formula:
- Average Speed = Total Distance / Total Time
- Average Speed = (2d) / (d / 36) = 2d * (36 / d) = 72 km/h
Conclusion
The average speed for the entire journey is 72 km/h, making option 'A' the correct answer.
To find the average speed for the entire journey, we use the formula:
Average Speed = Total Distance / Total Time
Step 1: Define the Distance
- Let the distance from city A to city B be "d" kilometers.
Step 2: Calculate Total Distance
- The total distance for the round trip is:
- Total Distance = d (to B) + d (return to A) = 2d
Step 3: Calculate Time for Each Leg of the Journey
- For the onward journey (A to B) at 60 km/h:
- Time = Distance / Speed = d / 60 hours
- For the return journey (B to A) at 90 km/h:
- Time = Distance / Speed = d / 90 hours
Step 4: Calculate Total Time
- Total Time = Time (to B) + Time (to A)
- Total Time = (d / 60) + (d / 90)
- To add these fractions, find a common denominator (which is 180):
- Total Time = (3d / 180) + (2d / 180) = (5d / 180) = (d / 36) hours
Step 5: Calculate Average Speed
- Now, substitute Total Distance and Total Time into the average speed formula:
- Average Speed = Total Distance / Total Time
- Average Speed = (2d) / (d / 36) = 2d * (36 / d) = 72 km/h
Conclusion
The average speed for the entire journey is 72 km/h, making option 'A' the correct answer.
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