A boat goes downstream from one station to another in 10 hours it covers the same distance upstream in 12 hours. If the speed of the stream be 2 km/h, find the speed of the boat.
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h, find the speed of the boat.
A boat goes downstream from one station to another in 10 hours it covers the same distance upstream in 12 hours. If the speed of the stream be 2 km/h, find the speed of the boat.
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Answer:
Let's denote the speed of the boat in still water as "B" km/h, and the speed of the stream as "S" km/h.
When the boat goes downstream, it benefits from the stream's current, so its effective speed is (B + S) km/h. When it goes upstream, it works against the current, so its effective speed is (B - S) km/h.
We are given that the boat takes 10 hours to cover the distance downstream and 12 hours to cover the same distance upstream.
Using the formula: Distance = Speed × Time
For downstream: Distance = (B + S) × 10
For upstream: Distance = (B - S) × 12
Since the distances are the same, we can set these two expressions equal to each other:
(B + S) × 10 = (B - S) × 12
Now, let's solve for B:
10(B + S) = 12(B - S)
Expand the equation:
10B + 10S = 12B - 12S
Now, bring the terms with "B" on one side and the terms with "S" on the other side:
10S + 12S = 12B - 10B
22S = 2B
Now, divide both sides by 2 to solve for B:
B = 22S / 2
B = 11S
We are given that the speed of the stream (S) is 2 km/h. Now, we can find the speed of the boat (B):
B = 11 × 2
B = 22 km/h
So, the speed of the boat in still water is 22 km/h.