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A boat travels upstream from B to A and downstream from A to B in 3 hours. If the speed of the boat in still water is 9 km/ h and the speed of the current is 3 km/h, the distance between A and B is
- a)9 km
- b)10 km
- c)11 km
- d)12 km
Correct answer is option 'D'. 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 ho...
Let the distance = d Speed of upstream = 9 – 3 = 6 km/h
Speed of down stream = 9 + 3 = 12 km/h
d = 12 km
Hence distance = 12 km
Speed of down stream = 9 + 3 = 12 km/h
d = 12 km
Hence distance = 12 km
Most Upvoted Answer
A boat travels upstream from B to A and downstream from A to B in 3 ho...
To solve this problem, we can use the formula:
Time = Distance / Speed
Let's denote the distance between points A and B as 'd'.
Speed of the boat in still water = 9 km/h
Speed of the current = 3 km/h
Upstream:
When the boat is traveling upstream from B to A, it is moving against the current. In this case, the effective speed of the boat is reduced by the speed of the current. So, the speed of the boat upstream is (9 - 3) = 6 km/h.
Downstream:
When the boat is traveling downstream from A to B, it is moving with the current. In this case, the effective speed of the boat is increased by the speed of the current. So, the speed of the boat downstream is (9 + 3) = 12 km/h.
Given that the boat takes 3 hours to travel both upstream and downstream, we can write the following equations:
Upstream: Time = Distance / Speed
3 = d / 6
Downstream: Time = Distance / Speed
3 = d / 12
Solving these equations, we can find the value of 'd':
Upstream: 3 = d / 6
Multiplying both sides by 6, we get:
18 = d
Downstream: 3 = d / 12
Multiplying both sides by 12, we get:
36 = d
Since the distance between A and B is the same in both cases, the value of 'd' must be the same. Therefore, the distance between A and B is 36 km.
Hence, the correct answer is option 'D', which is 12 km.
Time = Distance / Speed
Let's denote the distance between points A and B as 'd'.
Speed of the boat in still water = 9 km/h
Speed of the current = 3 km/h
Upstream:
When the boat is traveling upstream from B to A, it is moving against the current. In this case, the effective speed of the boat is reduced by the speed of the current. So, the speed of the boat upstream is (9 - 3) = 6 km/h.
Downstream:
When the boat is traveling downstream from A to B, it is moving with the current. In this case, the effective speed of the boat is increased by the speed of the current. So, the speed of the boat downstream is (9 + 3) = 12 km/h.
Given that the boat takes 3 hours to travel both upstream and downstream, we can write the following equations:
Upstream: Time = Distance / Speed
3 = d / 6
Downstream: Time = Distance / Speed
3 = d / 12
Solving these equations, we can find the value of 'd':
Upstream: 3 = d / 6
Multiplying both sides by 6, we get:
18 = d
Downstream: 3 = d / 12
Multiplying both sides by 12, we get:
36 = d
Since the distance between A and B is the same in both cases, the value of 'd' must be the same. Therefore, the distance between A and B is 36 km.
Hence, the correct answer is option 'D', which is 12 km.
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A boat travels upstream from B to A and downstream from A to B in 3 hours. If the speed of the boat in still water is 9 km/ h and the speed of the current is 3 km/h, the distance between A and B isa)9 kmb)10 kmc)11 kmd)12 kmCorrect answer is option 'D'. Can you explain this answer?
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