A boat can travel 114 miles upstream
in the same time that it can travel 186 miles downstream.
If the speed of the current is 6 miles per hour,
find the speed of the boat without a current.
any help would be greatly appreciated :)
Speed of boat in still water = V mi/h.
Speed of boat upstream = V-6 mi/h.
Speed of boat down stream = V+6 mi/h.
(V-6)t = 114 mi.
Eq1: Vt - 6t = 114.
(V+6)t = 186 mi.
Eq2: Vt + 6t = 186.
Add Eq1 and Eq2 and get:
2Vt = 300,
Vt = 150.
In Eq1, substitute 150 for Vt:
150 - 6t = 114,
-6t = 114 - 150 = -36,
t = 6h.
In Eq2, substitute 6 for t:
6V + 6*6 = 186,
6V + 36 = 186,
6V = 150,
V = 25mi/h.
To find the speed of the boat without a current, we'll need to use the formula for the speed of the boat in still water. Let's call the speed of the boat without a current "b" (in miles per hour).
When the boat is traveling upstream against the current, its effective speed is reduced by the speed of the current. So, the boat's speed upstream is (b - 6) miles per hour.
Similarly, when the boat is traveling downstream with the current, its effective speed is increased by the speed of the current. So, the boat's speed downstream is (b + 6) miles per hour.
Now, let's use the given information: the boat can travel 114 miles upstream in the same time that it can travel 186 miles downstream.
We can set up an equation using the formula for time:
Time upstream = Time downstream
Distance upstream / Speed upstream = Distance downstream / Speed downstream
114 / (b - 6) = 186 / (b + 6)
To solve this equation, we can cross-multiply:
114 * (b + 6) = 186 * (b - 6)
114b + 684 = 186b - 1116
72b = 1800
Dividing both sides by 72:
b = 25
Therefore, the speed of the boat without a current is 25 miles per hour.