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A rows a boat 100 km in 20 hours downstream and 72 km in upstream in 18 hours. Find the speed of the boat in still water.
- a)6.5 km/h
- b)4.5 km/h
- c)6 km/h
- d)7 km/h
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A rows a boat 100 km in 20 hours downstream and 72 km in upstream in 1...
Let speed of boat in still water is SB and speed of stream is SC and Speed of boat in upstream and downstream is SU and SD
Speed of boat in still water SB = 1/2 × (SD + SU)
⇒ 1/2 × (100/20 + 72/18)
⇒ 0.5 × (5 + 4)
∴ The speed of boat in still water = 4.5 km/hr
⇒ 1/2 × (100/20 + 72/18)
⇒ 0.5 × (5 + 4)
∴ The speed of boat in still water = 4.5 km/hr
Most Upvoted Answer
A rows a boat 100 km in 20 hours downstream and 72 km in upstream in 1...
Understanding the Problem
To find the speed of the boat in still water, we need to consider the speeds downstream and upstream separately.
Step 1: Calculate Downstream and Upstream Speeds
- Downstream Distance: 100 km
- Downstream Time: 20 hours
- Downstream Speed: Speed = Distance/Time = 100 km / 20 hours = 5 km/h
- Upstream Distance: 72 km
- Upstream Time: 18 hours
- Upstream Speed: Speed = Distance/Time = 72 km / 18 hours = 4 km/h
Step 2: Define Variables
- Let the speed of the boat in still water be 'b' km/h.
- Let the speed of the current be 'c' km/h.
Step 3: Set Up Equations
- Downstream Speed Equation: b + c = 5 km/h
- Upstream Speed Equation: b - c = 4 km/h
Step 4: Solve the Equations
1. From the first equation: b + c = 5
2. From the second equation: b - c = 4
Now, add both equations:
- (b + c) + (b - c) = 5 + 4
- 2b = 9
- b = 9/2 = 4.5 km/h
Conclusion
The speed of the boat in still water is 4.5 km/h. Thus, the correct answer is option 'B'.
To find the speed of the boat in still water, we need to consider the speeds downstream and upstream separately.
Step 1: Calculate Downstream and Upstream Speeds
- Downstream Distance: 100 km
- Downstream Time: 20 hours
- Downstream Speed: Speed = Distance/Time = 100 km / 20 hours = 5 km/h
- Upstream Distance: 72 km
- Upstream Time: 18 hours
- Upstream Speed: Speed = Distance/Time = 72 km / 18 hours = 4 km/h
Step 2: Define Variables
- Let the speed of the boat in still water be 'b' km/h.
- Let the speed of the current be 'c' km/h.
Step 3: Set Up Equations
- Downstream Speed Equation: b + c = 5 km/h
- Upstream Speed Equation: b - c = 4 km/h
Step 4: Solve the Equations
1. From the first equation: b + c = 5
2. From the second equation: b - c = 4
Now, add both equations:
- (b + c) + (b - c) = 5 + 4
- 2b = 9
- b = 9/2 = 4.5 km/h
Conclusion
The speed of the boat in still water is 4.5 km/h. Thus, the correct answer is option 'B'.
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A rows a boat 100 km in 20 hours downstream and 72 km in upstream in 18 hours. Find the speed of the boat in still water.a)6.5 km/hb)4.5 km/hc)6 km/hd)7 km/hCorrect answer is option 'B'. Can you explain this answer?
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