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A boat takes 5 hours to row downstream along the entire length of the river. If the speed of the stream increases by 1 km/hr and the speed of the boat remains the same, the boat will take 40 hours to row upstream along the entire length of the river. If the speed of boat in still water is 5 km/hr, find the length of the river (in km).
- a)30
- b)40
- c)20
- d)80
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A boat takes 5 hours to row downstream along the entire length of the ...
Let the speed of stream be x km/hr.
∴ Length of the river = (5 + x) x 5 = (5x + 25) km
Also, [5 - (x + 1)] x 40 = 5x + 25
Solving this we get, x = 3 km/hr
∴ Length of the river = (5 x 3 + 25) = 40 km
Answer: 40
Hence Option 2
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A boat takes 5 hours to row downstream along the entire length of the ...
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A boat takes 5 hours to row downstream along the entire length of the ...
Let's assume the length of the river is 'd' km.
Given:
Speed of boat in still water = 5 km/hr
Time taken to row downstream = 5 hours
Time taken to row upstream = 40 hours
Let's denote the speed of the stream as 's' km/hr.
Downstream:
When the boat is rowing downstream, the effective speed of the boat is the sum of the speed of the boat in still water and the speed of the stream.
So, the effective speed of the boat downstream is (5 + s) km/hr.
We know that speed = distance/time.
Therefore, the distance travelled downstream is given by:
Distance downstream = (5 + s) km/hr * 5 hr = 5(5 + s) km
Upstream:
When the boat is rowing upstream, the effective speed of the boat is the difference between the speed of the boat in still water and the speed of the stream.
So, the effective speed of the boat upstream is (5 - s) km/hr.
We know that speed = distance/time.
Therefore, the distance travelled upstream is given by:
Distance upstream = (5 - s) km/hr * 40 hr = 40(5 - s) km
Since the boat takes the entire length of the river to row downstream and upstream, we can equate the distances:
5(5 + s) km = 40(5 - s) km
Simplifying the equation, we get:
25 + 5s = 200 - 40s
45s = 175
s = 175/45
s ≈ 3.89 km/hr
Now, we can substitute the value of 's' back into one of the equations to find the length of the river 'd':
Distance downstream = (5 + 3.89) km/hr * 5 hr = 9.45 km
Therefore, the length of the river is approximately 9.45 km, which is closest to 40 km (option B).
Given:
Speed of boat in still water = 5 km/hr
Time taken to row downstream = 5 hours
Time taken to row upstream = 40 hours
Let's denote the speed of the stream as 's' km/hr.
Downstream:
When the boat is rowing downstream, the effective speed of the boat is the sum of the speed of the boat in still water and the speed of the stream.
So, the effective speed of the boat downstream is (5 + s) km/hr.
We know that speed = distance/time.
Therefore, the distance travelled downstream is given by:
Distance downstream = (5 + s) km/hr * 5 hr = 5(5 + s) km
Upstream:
When the boat is rowing upstream, the effective speed of the boat is the difference between the speed of the boat in still water and the speed of the stream.
So, the effective speed of the boat upstream is (5 - s) km/hr.
We know that speed = distance/time.
Therefore, the distance travelled upstream is given by:
Distance upstream = (5 - s) km/hr * 40 hr = 40(5 - s) km
Since the boat takes the entire length of the river to row downstream and upstream, we can equate the distances:
5(5 + s) km = 40(5 - s) km
Simplifying the equation, we get:
25 + 5s = 200 - 40s
45s = 175
s = 175/45
s ≈ 3.89 km/hr
Now, we can substitute the value of 's' back into one of the equations to find the length of the river 'd':
Distance downstream = (5 + 3.89) km/hr * 5 hr = 9.45 km
Therefore, the length of the river is approximately 9.45 km, which is closest to 40 km (option B).
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A boat takes 5 hours to row downstream along the entire length of the river. If the speed of the stream increases by 1 km/hr and the speed of the boat remains the same, the boat will take 40 hours to row upstream along the entire length of the river. If the speed of boat in still water is 5 km/hr, find the length of the river (in km).a)30b)40c)20d)80Correct answer is option 'B'. Can you explain this answer?
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