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A boat can cover 60 km downstream in 2 hours when its engine is working and 10 km in 2 hours with the flow (when the engine is off). What is the upstream speed of the boat?
- a)8 km/hr
- b)10 km/hr
- c)12 km/hr
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A boat can cover 60 km downstream in 2 hours when its engine is workin...
Understanding the Problem
To find the upstream speed of the boat, we first need to determine the downstream and upstream speeds based on the given information.
Downstream Speed Calculation
- The boat covers 60 km downstream in 2 hours.
- Therefore, the downstream speed (Speed_down) is calculated as:
\[ \text{Speed_down} = \frac{60 \text{ km}}{2 \text{ hours}} = 30 \text{ km/hr} \]
Flow Speed Calculation
- The boat covers 10 km in 2 hours with the flow (engine off).
- Thus, the flow speed (Speed_flow) is:
\[ \text{Speed_flow} = \frac{10 \text{ km}}{2 \text{ hours}} = 5 \text{ km/hr} \]
Upstream Speed Calculation
- The downstream speed is the sum of the boat's speed in still water (Speed_boat) and the flow speed:
\[ \text{Speed_down} = \text{Speed_boat} + \text{Speed_flow} \]
\[ 30 \text{ km/hr} = \text{Speed_boat} + 5 \text{ km/hr} \]
\[ \text{Speed_boat} = 30 \text{ km/hr} - 5 \text{ km/hr} = 25 \text{ km/hr} \]
- The upstream speed is the boat's speed in still water minus the flow speed:
\[ \text{Speed_up} = \text{Speed_boat} - \text{Speed_flow} \]
\[ \text{Speed_up} = 25 \text{ km/hr} - 5 \text{ km/hr} = 20 \text{ km/hr} \]
Final Conclusion
- The calculated upstream speed is 20 km/hr. However, it seems there was an error in interpreting the question, leading to the answer being marked as 'D' (None of these).
Thus, the upstream speed of the boat is indeed 20 km/hr, but given the context of the question and provided options, the correct answer is option 'D' stating that it does not match the given choices.
To find the upstream speed of the boat, we first need to determine the downstream and upstream speeds based on the given information.
Downstream Speed Calculation
- The boat covers 60 km downstream in 2 hours.
- Therefore, the downstream speed (Speed_down) is calculated as:
\[ \text{Speed_down} = \frac{60 \text{ km}}{2 \text{ hours}} = 30 \text{ km/hr} \]
Flow Speed Calculation
- The boat covers 10 km in 2 hours with the flow (engine off).
- Thus, the flow speed (Speed_flow) is:
\[ \text{Speed_flow} = \frac{10 \text{ km}}{2 \text{ hours}} = 5 \text{ km/hr} \]
Upstream Speed Calculation
- The downstream speed is the sum of the boat's speed in still water (Speed_boat) and the flow speed:
\[ \text{Speed_down} = \text{Speed_boat} + \text{Speed_flow} \]
\[ 30 \text{ km/hr} = \text{Speed_boat} + 5 \text{ km/hr} \]
\[ \text{Speed_boat} = 30 \text{ km/hr} - 5 \text{ km/hr} = 25 \text{ km/hr} \]
- The upstream speed is the boat's speed in still water minus the flow speed:
\[ \text{Speed_up} = \text{Speed_boat} - \text{Speed_flow} \]
\[ \text{Speed_up} = 25 \text{ km/hr} - 5 \text{ km/hr} = 20 \text{ km/hr} \]
Final Conclusion
- The calculated upstream speed is 20 km/hr. However, it seems there was an error in interpreting the question, leading to the answer being marked as 'D' (None of these).
Thus, the upstream speed of the boat is indeed 20 km/hr, but given the context of the question and provided options, the correct answer is option 'D' stating that it does not match the given choices.
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Community Answer
A boat can cover 60 km downstream in 2 hours when its engine is workin...
Reqd. speed = 30 – 5 × 2 = 20 km/hr
Hence, Option D is correct.
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A boat can cover 60 km downstream in 2 hours when its engine is working and 10 km in 2 hours with the flow (when the engine is off). What is the upstream speed of the boat?a)8 km/hrb)10 km/hrc)12 km/hrd)None of theseCorrect answer is option 'D'. Can you explain this answer?
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