A boat can travel at a speed of 13 km/h in still water. If the speed of the stream is 4 km/h, then the time taken by boat to go 63 km in the opposite direction to stream is:
7 hours
Here's how to solve this problem step-by-step:
1. Determine the boat's speed against the stream (upstream):
- Speed of the boat in still water = 13 km/h
- Speed of the stream = 4 km/h
- Speed of the boat against the stream (upstream speed) = Speed of boat in still water - Speed of the stream
- Upstream speed = 13 km/h - 4 km/h = 9 km/h
2. Calculate the time taken to travel 63 km upstream:
- Distance = 63 km
- Speed = 9 km/h
- Time = Distance / Speed
- Time = 63 km / 9 km/h = 7 hours
Therefore, the time taken by the boat to go 63 km in the opposite direction to the stream is 7 hours.
The correct answer is 7 hours.
7 hours
Step-by-step Detailed Solution:
Step 1: Identify Given Information
- Speed of boat in still water, \( B = 13\, \text{km/h} \)
- Speed of stream, \( S = 4\, \text{km/h} \)
- Distance, \( D = 63\, \text{km} \)
- The boat travels opposite (against) the stream.
Step 2: Calculate Effective Speed (upstream)
When traveling against the stream (upstream):
\[ \text{Effective Speed (Upstream)} = B - S \]
Substituting given values:
\[ = 13\,\text{km/h} - 4\,\text{km/h} = 9\,\text{km/h} \]
Step 3: Calculate Time Taken
Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substitute values:
\[ \text{Time} = \frac{63\,\text{km}}{9\,\text{km/h}} = 7\,\text{hours} \]
✅ Final Answer:
🎯 7 hours
7 hours
Given:
- Boat speed in still water (B) = 13 km/h
- Stream speed (S) = 4 km/h
- Distance (D) = 63 km (against stream)
Solution:
Step 1: Calculate Upstream Speed
When moving against the stream, the effective speed decreases:
\[ \text{Speed}_{\text{upstream}} = B - S = 13\,\text{km/h} - 4\,\text{km/h} = 9\,\text{km/h} \]
Step 2: Calculate Time Taken
Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{63\,\text{km}}{9\,\text{km/h}} = 7\,\text{hours} \]
Conclusion:
The boat takes 7 hours to travel 63 km upstream.
Verification:
Distance covered in 7 hours at 9 km/h:
\[ 9\,\text{km/h} \times 7\,\text{h} = 63\,\text{km} \quad \text{(matches given distance)} \]
Final Answer:
✅ 7 hours
Important Questions from Boat and River
A boat goes 30 km upstream in 3 hours and downstream in 1 hour. How much time (in hours) will this boat take to cover 60 km in still water?
The speed of a motorboat in still water is 20 km/h. It travels 150 km downstream and then returns to the starting point. If the round trip takes a total of 16 hours, what is the speed (in km/h) of the flow of river?
The time taken by a boat to travel 13 km downstream is the same as time taken by it to travel 7 km upstream. If the speed of the stream is 3 km/h, then how much time (in hours) will it take to travel a distance of 44.8 km in still water?
A man can row a distance of 8 km downstream in a certain time and can row 6 km upstream in the same time. If he rows 24 km upstream and the same distance downstream in \(1\frac{3}{4}\) hours, then the speed (in km/h) of the current is:
A boat goes 27 km upstream and 33 km downstream in 6 hours. In the same time it can go 36 km upstream and 22 km downstream. How much time will it take to go 36 km upstream and 44 km downstream?
