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A motor car goes from Mumbai to Pune at a speed of 20 km/h and comes back from there at a speed of 30 km/h. What is the average speed of the car for the whole journey?
- a)26 km/h
- b)25 km/h
- c)24 km/h
- d)23 km/h
- e)None of the above/More than one of the above
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A motor car goes from Mumbai to Pune at a speed of 20 km/h and comes b...
Solution:
To find the average speed of the car for the whole journey, we need to calculate the total distance traveled and divide it by the total time taken.
Let's assume the distance between Mumbai and Pune is 'd' km.
1. Calculate the time taken to travel from Mumbai to Pune:
- Speed = 20 km/h
- Time = Distance / Speed = d / 20
2. Calculate the time taken to travel from Pune to Mumbai:
- Speed = 30 km/h
- Time = Distance / Speed = d / 30
3. Calculate the total distance traveled:
- Total distance = Distance from Mumbai to Pune + Distance from Pune to Mumbai = d + d = 2d
4. Calculate the total time taken:
- Total time = Time taken from Mumbai to Pune + Time taken from Pune to Mumbai = d / 20 + d / 30
5. Calculate the average speed:
- Average speed = Total distance / Total time = 2d / (d/20 + d/30)
To simplify the expression, we can find the least common multiple (LCM) of 20 and 30, which is 60.
- Average speed = 2d / (d/20 + d/30)
= 2d / (3d/60 + 2d/60)
= 2d / (5d/60)
= 2d * 60 / 5d
= 120d / 5d
= 24 km/h
Therefore, the average speed of the car for the whole journey is 24 km/h (option C).
To find the average speed of the car for the whole journey, we need to calculate the total distance traveled and divide it by the total time taken.
Let's assume the distance between Mumbai and Pune is 'd' km.
1. Calculate the time taken to travel from Mumbai to Pune:
- Speed = 20 km/h
- Time = Distance / Speed = d / 20
2. Calculate the time taken to travel from Pune to Mumbai:
- Speed = 30 km/h
- Time = Distance / Speed = d / 30
3. Calculate the total distance traveled:
- Total distance = Distance from Mumbai to Pune + Distance from Pune to Mumbai = d + d = 2d
4. Calculate the total time taken:
- Total time = Time taken from Mumbai to Pune + Time taken from Pune to Mumbai = d / 20 + d / 30
5. Calculate the average speed:
- Average speed = Total distance / Total time = 2d / (d/20 + d/30)
To simplify the expression, we can find the least common multiple (LCM) of 20 and 30, which is 60.
- Average speed = 2d / (d/20 + d/30)
= 2d / (3d/60 + 2d/60)
= 2d / (5d/60)
= 2d * 60 / 5d
= 120d / 5d
= 24 km/h
Therefore, the average speed of the car for the whole journey is 24 km/h (option C).
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Community Answer
A motor car goes from Mumbai to Pune at a speed of 20 km/h and comes b...
Formula-Free approach:
Let the distance between Mumbai and Pune be the LCM of 20 and 30 which is 60km.
So, time taken in going from Mumbai to Pune
⇒ 60/20 = 3 hrs.
Time taken in coming back from Pune to Mumbai
⇒ 60/30 = 2 hrs.
Now,
Average speed = Total Distance/Total time taken ⇒ (60+60)/(3+2) = 120/5
⇒ 24km/hr
Formula Approach:
For two equal distances, formula is:
Average Speed = 2×(a×b)/(a+b)
Where a and b are the speeds during each distance.
Now, applying values from given question:
Average Speed = 2×20×30/(20+30)
⇒ 1200/50 = 24km/hr
Hence, option(3) is the correct answer.
Let the distance between Mumbai and Pune be the LCM of 20 and 30 which is 60km.
So, time taken in going from Mumbai to Pune
⇒ 60/20 = 3 hrs.
Time taken in coming back from Pune to Mumbai
⇒ 60/30 = 2 hrs.
Now,
Average speed = Total Distance/Total time taken ⇒ (60+60)/(3+2) = 120/5
⇒ 24km/hr
Formula Approach:
For two equal distances, formula is:
Average Speed = 2×(a×b)/(a+b)
Where a and b are the speeds during each distance.
Now, applying values from given question:
Average Speed = 2×20×30/(20+30)
⇒ 1200/50 = 24km/hr
Hence, option(3) is the correct answer.
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