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A boat running downstream covers a distance of 20 kms in 2 hours. While coming back the boat takes 4 hours to cover the same distance. What is the speed of the boat in still water in kmph?
- a)6.5
- b)7.5
- c)8.5
- d)9
Correct answer is option 'B'. Can you explain this answer?
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A boat running downstream covers a distance of 20 kms in 2 hours. Whil...
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A boat running downstream covers a distance of 20 kms in 2 hours. Whil...
Given:
- Distance covered downstream = 20 km
- Time taken downstream = 2 hours
- Time taken upstream = 4 hours
To find:
- Speed of the boat in still water
Let's assume the speed of the boat in still water is 'x' km/hr and the speed of the current is 'y' km/hr.
Speed downstream:
When the boat is going downstream, it gets the additional speed of the current, so the effective speed becomes (x + y) km/hr.
Since distance = speed × time, we can write:
Distance downstream = (x + y) × 2
Speed upstream:
When the boat is going upstream, it opposes the current, so the effective speed becomes (x - y) km/hr.
Since distance = speed × time, we can write:
Distance upstream = (x - y) × 4
Equation 1:
From the given information, we know that the distance downstream is 20 km and the time taken is 2 hours. Substituting these values in the equation, we get:
20 = (x + y) × 2
Equation 2:
Similarly, the distance upstream is also 20 km and the time taken is 4 hours. Substituting these values in the equation, we get:
20 = (x - y) × 4
Solving the equations:
We have two equations and two variables (x and y), so we can solve these equations simultaneously to find the values of x and y.
From Equation 1, we can rewrite it as:
x + y = 10 ...(Equation 3)
From Equation 2, we can rewrite it as:
x - y = 5 ...(Equation 4)
Adding Equation 3 and Equation 4, we get:
2x = 15
Dividing both sides by 2, we get:
x = 7.5
Therefore, the speed of the boat in still water is 7.5 km/hr.
Hence, the correct answer is option B) 7.5.
- Distance covered downstream = 20 km
- Time taken downstream = 2 hours
- Time taken upstream = 4 hours
To find:
- Speed of the boat in still water
Let's assume the speed of the boat in still water is 'x' km/hr and the speed of the current is 'y' km/hr.
Speed downstream:
When the boat is going downstream, it gets the additional speed of the current, so the effective speed becomes (x + y) km/hr.
Since distance = speed × time, we can write:
Distance downstream = (x + y) × 2
Speed upstream:
When the boat is going upstream, it opposes the current, so the effective speed becomes (x - y) km/hr.
Since distance = speed × time, we can write:
Distance upstream = (x - y) × 4
Equation 1:
From the given information, we know that the distance downstream is 20 km and the time taken is 2 hours. Substituting these values in the equation, we get:
20 = (x + y) × 2
Equation 2:
Similarly, the distance upstream is also 20 km and the time taken is 4 hours. Substituting these values in the equation, we get:
20 = (x - y) × 4
Solving the equations:
We have two equations and two variables (x and y), so we can solve these equations simultaneously to find the values of x and y.
From Equation 1, we can rewrite it as:
x + y = 10 ...(Equation 3)
From Equation 2, we can rewrite it as:
x - y = 5 ...(Equation 4)
Adding Equation 3 and Equation 4, we get:
2x = 15
Dividing both sides by 2, we get:
x = 7.5
Therefore, the speed of the boat in still water is 7.5 km/hr.
Hence, the correct answer is option B) 7.5.
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A boat running downstream covers a distance of 20 kms in 2 hours. While coming back the boat takes 4 hours to cover the same distance. What is the speed of the boat in still water in kmph?a)6.5b)7.5c)8.5d)9Correct answer is option 'B'. Can you explain this answer?
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