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If a boat goes upstream at a speed of 18 km/hr and comes back the same distance at 30 km/hr, then what is the average speed (in km/hr) for the total journey?
- a)22.5
- b)24
- c)20.5
- d)25
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If a boat goes upstream at a speed of 18 km/hr and comes back the sam...
Given:
- Speed of the boat upstream = 18 km/hr
- Speed of the boat downstream = 30 km/hr
To find:
- Average speed for the total journey
Concept:
- Average speed is defined as the total distance traveled divided by the total time taken.
- When a boat travels a certain distance upstream and then returns the same distance downstream, the time taken for the upstream journey will be greater than the time taken for the downstream journey.
Calculation:
Let's assume the distance traveled by the boat in one direction is D km.
1. Time taken for the upstream journey:
- Speed = 18 km/hr
- Distance = D km
- Time = Distance / Speed = D / 18
2. Time taken for the downstream journey:
- Speed = 30 km/hr
- Distance = D km
- Time = Distance / Speed = D / 30
3. Total time taken for the journey:
- Total time = Time taken upstream + Time taken downstream = D / 18 + D / 30
4. Average speed for the total journey:
- Average speed = Total distance / Total time
- Total distance = Distance upstream + Distance downstream = D + D = 2D
- Average speed = (2D) / (D / 18 + D / 30)
To simplify this expression, we can find the least common multiple (LCM) of 18 and 30, which is 90.
- Average speed = (2D) / (D / 18 + D / 30)
- Average speed = (2D) / (5D / 90 + 3D / 90)
- Average speed = (2D) / (8D / 90)
- Average speed = (2D) * (90 / 8D)
- Average speed = 2 * 90 / 8 = 45 / 4 = 11.25 km/hr
Therefore, the average speed for the total journey is 11.25 km/hr, which is closest to option 'A' (22.5 km/hr).
- Speed of the boat upstream = 18 km/hr
- Speed of the boat downstream = 30 km/hr
To find:
- Average speed for the total journey
Concept:
- Average speed is defined as the total distance traveled divided by the total time taken.
- When a boat travels a certain distance upstream and then returns the same distance downstream, the time taken for the upstream journey will be greater than the time taken for the downstream journey.
Calculation:
Let's assume the distance traveled by the boat in one direction is D km.
1. Time taken for the upstream journey:
- Speed = 18 km/hr
- Distance = D km
- Time = Distance / Speed = D / 18
2. Time taken for the downstream journey:
- Speed = 30 km/hr
- Distance = D km
- Time = Distance / Speed = D / 30
3. Total time taken for the journey:
- Total time = Time taken upstream + Time taken downstream = D / 18 + D / 30
4. Average speed for the total journey:
- Average speed = Total distance / Total time
- Total distance = Distance upstream + Distance downstream = D + D = 2D
- Average speed = (2D) / (D / 18 + D / 30)
To simplify this expression, we can find the least common multiple (LCM) of 18 and 30, which is 90.
- Average speed = (2D) / (D / 18 + D / 30)
- Average speed = (2D) / (5D / 90 + 3D / 90)
- Average speed = (2D) / (8D / 90)
- Average speed = (2D) * (90 / 8D)
- Average speed = 2 * 90 / 8 = 45 / 4 = 11.25 km/hr
Therefore, the average speed for the total journey is 11.25 km/hr, which is closest to option 'A' (22.5 km/hr).
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Community Answer
If a boat goes upstream at a speed of 18 km/hr and comes back the sam...
Let upstream speed = a and downstream speed = b
Average speed = 
= 22.5 km/hr
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If a boat goes upstream at a speed of 18 km/hr and comes back the same distance at 30 km/hr, then what is the average speed (in km/hr) for the total journey?a)22.5b)24c)20.5d)25Correct answer is option 'A'. Can you explain this answer?
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