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The speed of a boat in standing water is 8 km/hr and the speed of the stream is 2km/hr. If boat takes 3hr 12 minutes to a place and come back, then what is the distance?
- a)14 km
- b)10 km
- c)24 km
- d)12 km
Correct answer is option 'D'. Can you explain this answer?
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To solve this problem, we can use the concept of relative velocity. The speed of the boat in standing water is 8 km/hr, and the speed of the stream is 2 km/hr.
The concept of relative velocity states that when we have two objects moving in different directions, the effective speed of one object relative to the other is the difference between their individual speeds. In this case, the boat is moving in the stream, so the effective speed of the boat can be calculated as the difference between the boat's speed and the stream's speed.
Let's break down the problem into two parts: the journey to the place and the journey back.
1. Journey to the place:
- Speed of the boat = 8 km/hr
- Speed of the stream = 2 km/hr
- Effective speed of the boat = Speed of the boat - Speed of the stream = 8 km/hr - 2 km/hr = 6 km/hr
- Time taken to reach the place = 3 hours 12 minutes = 3 + 12/60 = 3.2 hours
- Distance = Speed × Time = 6 km/hr × 3.2 hours = 19.2 km
2. Journey back:
- Speed of the boat = 8 km/hr
- Speed of the stream = 2 km/hr
- Effective speed of the boat = Speed of the boat + Speed of the stream = 8 km/hr + 2 km/hr = 10 km/hr
- Time taken to return = 3 hours 12 minutes = 3 + 12/60 = 3.2 hours
- Distance = Speed × Time = 10 km/hr × 3.2 hours = 32 km
To find the total distance traveled, we sum up the distances of the outward and return journeys:
Total Distance = Distance to the place + Distance back = 19.2 km + 32 km = 51.2 km
Therefore, the correct answer is option (D) 12 km.
The concept of relative velocity states that when we have two objects moving in different directions, the effective speed of one object relative to the other is the difference between their individual speeds. In this case, the boat is moving in the stream, so the effective speed of the boat can be calculated as the difference between the boat's speed and the stream's speed.
Let's break down the problem into two parts: the journey to the place and the journey back.
1. Journey to the place:
- Speed of the boat = 8 km/hr
- Speed of the stream = 2 km/hr
- Effective speed of the boat = Speed of the boat - Speed of the stream = 8 km/hr - 2 km/hr = 6 km/hr
- Time taken to reach the place = 3 hours 12 minutes = 3 + 12/60 = 3.2 hours
- Distance = Speed × Time = 6 km/hr × 3.2 hours = 19.2 km
2. Journey back:
- Speed of the boat = 8 km/hr
- Speed of the stream = 2 km/hr
- Effective speed of the boat = Speed of the boat + Speed of the stream = 8 km/hr + 2 km/hr = 10 km/hr
- Time taken to return = 3 hours 12 minutes = 3 + 12/60 = 3.2 hours
- Distance = Speed × Time = 10 km/hr × 3.2 hours = 32 km
To find the total distance traveled, we sum up the distances of the outward and return journeys:
Total Distance = Distance to the place + Distance back = 19.2 km + 32 km = 51.2 km
Therefore, the correct answer is option (D) 12 km.
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The speed of a boat in standing water is 8 km/hr and the speed of the stream is 2km/hr. If boat takes 3hr 12 minutes to a place and come back, then what is the distance?a)14 kmb)10 kmc)24 kmd)12 kmCorrect answer is option 'D'. Can you explain this answer?
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