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A man can swim upstream at a speed of 4 km/hr and downstream at 8 km/hr. In how much time will he cover a distance of 3 km in still water?
- a)10 min
- b)20 min
- c)30 min
- d)40 min
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A man can swim upstream at a speed of 4 km/hr and downstream at 8 km/h...
Upstream speed = 4 km/hr
Downstream speed = 10 km/hr
Speed in still water = ½ × (downstream speed + upstream speed) = ½ × (8 + 4) = 6 km/hr
∴ Required time = 3/6 = 0.5 hrs = 30 min
Downstream speed = 10 km/hr
Speed in still water = ½ × (downstream speed + upstream speed) = ½ × (8 + 4) = 6 km/hr
∴ Required time = 3/6 = 0.5 hrs = 30 min
Most Upvoted Answer
A man can swim upstream at a speed of 4 km/hr and downstream at 8 km/h...
To solve this problem, we need to consider the velocity of the man relative to the ground and the velocity of the river current. The velocity of the man relative to the ground can be calculated using the Pythagorean theorem.
Let's break down the problem into the given information and the solution steps.
Given:
- Velocity of the man in still water: 4.0 km/hr
- Width of the river: 1.0 km
- Velocity of the river current: 3.0 km/hr
Solution:
1. Calculate the resultant velocity of the man relative to the ground using the Pythagorean theorem:
- Let v be the velocity of the man in still water and c be the velocity of the river current.
- The resultant velocity of the man relative to the ground is given by √(v^2 + c^2).
- Substituting the given values, we have √(4.0^2 + 3.0^2) = √(16.0 + 9.0) = √25.0 = 5.0 km/hr.
2. Calculate the time taken to cross the river:
- The distance to be crossed is 1.0 km.
- The speed at which the man is crossing the river is the component of the resultant velocity perpendicular to the river current, which can be calculated using trigonometry.
- The component of the resultant velocity perpendicular to the river current is given by v * (c / √(v^2 + c^2)).
- Substituting the given values, we have 4.0 * (3.0 / 5.0) = 2.4 km/hr.
- The time taken to cross the river is equal to the distance divided by the speed, which is 1.0 km / 2.4 km/hr.
- Converting km/hr to km/min, we have (1.0 km / 2.4 km/hr) * (60 min/hr) = 25 min.
Therefore, the correct answer is option C) 15 min.
Let's break down the problem into the given information and the solution steps.
Given:
- Velocity of the man in still water: 4.0 km/hr
- Width of the river: 1.0 km
- Velocity of the river current: 3.0 km/hr
Solution:
1. Calculate the resultant velocity of the man relative to the ground using the Pythagorean theorem:
- Let v be the velocity of the man in still water and c be the velocity of the river current.
- The resultant velocity of the man relative to the ground is given by √(v^2 + c^2).
- Substituting the given values, we have √(4.0^2 + 3.0^2) = √(16.0 + 9.0) = √25.0 = 5.0 km/hr.
2. Calculate the time taken to cross the river:
- The distance to be crossed is 1.0 km.
- The speed at which the man is crossing the river is the component of the resultant velocity perpendicular to the river current, which can be calculated using trigonometry.
- The component of the resultant velocity perpendicular to the river current is given by v * (c / √(v^2 + c^2)).
- Substituting the given values, we have 4.0 * (3.0 / 5.0) = 2.4 km/hr.
- The time taken to cross the river is equal to the distance divided by the speed, which is 1.0 km / 2.4 km/hr.
- Converting km/hr to km/min, we have (1.0 km / 2.4 km/hr) * (60 min/hr) = 25 min.
Therefore, the correct answer is option C) 15 min.
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A man can swim upstream at a speed of 4 km/hr and downstream at 8 km/hr. In how much time will he cover a distance of 3 km in still water?a)10 minb)20 minc)30 mind)40 minCorrect answer is option 'C'. Can you explain this answer?
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