A Coast-Guard patrol boat travels 4 hr on a trip downstream with a 6-mph current. The return trip against the same current
takes 5 hr. Find the speed of the boat in still water
The downstream speed with respect to land is V+6 and the upstream speed is V-6, where V is the speed in still water.
Let the distance be D
D/(V+6) = 4 hrs
D/(V-6) = 5
4(V+6) = 5(V-6)
V = 54 mph
To find the speed of the boat in still water, we can use the concept of relative velocity.
Let's denote the speed of the boat in still water as 'b' and the speed of the current as 'c'.
When the boat travels downstream, it benefits from the current, so its effective speed is increased. In this case, the effective speed is the sum of the speed of the boat in still water and the speed of the current. So, the speed downstream can be represented as b + c.
When the boat travels upstream against the current, it has to overcome the opposing force of the current, so its effective speed is reduced. In this case, the effective speed is the difference between the speed of the boat in still water and the speed of the current. So, the speed upstream can be represented as b - c.
Given that the boat travels downstream for 4 hours at a speed of b + c, and it travels upstream for 5 hours at a speed of b - c, we can set up the following equations:
4(b + c) = 5(b - c)
Now, we can simplify and solve for 'b':
4b + 4c = 5b - 5c
4c + 5c = 5b - 4b
9c = b
So, the speed of the boat in still water is 9 times the speed of the current.
To find the exact speed of the boat, we need the value of the current speed.