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A boat travels upstream from B to A and downstream from A to B in 3 hrs. If the speed of the boat in still water is 9 km/hr and the speed of the current is 3 km/hr, the distance between A and B is
- a)8 km
- b)16 km
- c)12 km
- d)cannot be determined
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A boat travels upstream from B to A and downstream from A to B in 3 hr...
Most Upvoted Answer
A boat travels upstream from B to A and downstream from A to B in 3 hr...
Approach:
To solve this problem, we can use the formula Distance = Speed × Time. We will calculate the time taken for each leg of the journey and then use the given information to find the distance between points A and B.
Calculations:
Upstream Journey (B to A):
- Speed of boat in still water = 9 km/hr
- Speed of current = 3 km/hr
- Speed upstream = 9 km/hr - 3 km/hr = 6 km/hr
- Time taken for upstream journey = Distance / Speed = x / 6
Downstream Journey (A to B):
- Speed downstream = 9 km/hr + 3 km/hr = 12 km/hr
- Time taken for downstream journey = Distance / Speed = x / 12
Given that the total time taken for the round trip is 3 hours:
x / 6 + x / 12 = 3
Solving this equation, we get:
2x + x = 36
3x = 36
x = 12 km
Therefore, the distance between points A and B is 12 km. Hence, the correct answer is option C) 12 km.
To solve this problem, we can use the formula Distance = Speed × Time. We will calculate the time taken for each leg of the journey and then use the given information to find the distance between points A and B.
Calculations:
Upstream Journey (B to A):
- Speed of boat in still water = 9 km/hr
- Speed of current = 3 km/hr
- Speed upstream = 9 km/hr - 3 km/hr = 6 km/hr
- Time taken for upstream journey = Distance / Speed = x / 6
Downstream Journey (A to B):
- Speed downstream = 9 km/hr + 3 km/hr = 12 km/hr
- Time taken for downstream journey = Distance / Speed = x / 12
Given that the total time taken for the round trip is 3 hours:
x / 6 + x / 12 = 3
Solving this equation, we get:
2x + x = 36
3x = 36
x = 12 km
Therefore, the distance between points A and B is 12 km. Hence, the correct answer is option C) 12 km.
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