A boat cruises downstream for 2 hours before heading back. It takes 3.5 hours going upstream to get back. If the speed of the stream is 8 mph, what is the speed of the boat in still water?:
To solve this problem, we need to understand the concept of relative speed. The speed of an object in still water is the speed at which it travels in the absence of any external factors, such as a current or wind. The speed of the stream is the rate at which the water in the river flows.
Let's assume the speed of the boat in still water is "B" mph.
When the boat is cruising downstream, it benefits from the speed of the stream. So, the effective speed of the boat is the sum of its speed in still water and the speed of the stream, which is (B + 8) mph. If it takes 2 hours to travel downstream, the distance covered will be (2 * (B + 8)) miles.
When the boat is going upstream against the current, it has to overcome the speed of the stream. So, the effective speed of the boat is the difference between its speed in still water and the speed of the stream, which is (B - 8) mph. If it takes 3.5 hours to travel upstream, the distance covered will be (3.5 * (B - 8)) miles.
Since the distances covered going downstream and upstream are the same (as they are the boat's round trip), we can equate the two distances and solve for B:
2 * (B + 8) = 3.5 * (B - 8)
Simplifying the equation:
2B + 16 = 3.5B - 28
Grouping like terms:
3.5B - 2B = 16 + 28
1.5B = 44
Dividing both sides of the equation by 1.5:
B = 44 / 1.5
B ≈ 29.33
Therefore, the speed of the boat in still water is approximately 29.33 mph.