A boat, which moves at 18 mph in still water, travels 14 miles downstream in the same amount of time it takes to travel 10 miles upstream. Find the speed of the current.
Let c be the speed of the current. When traveling downstream, the boat's effective speed is 18+c mph, and when traveling upstream, the boat's effective speed is 18-c mph.
The time it takes the boat to travel 14 miles downstream is 14/(18+c) hours, and the time it takes the boat to travel 10 miles upstream is 10/(18-c) hours. Since the problem states that these times are equal, we can set up an equation:
14/(18+c) = 10/(18-c)
Now we can solve for c:
14*(18-c) = 10*(18+c)
252 - 14c = 180 + 10c
72 = 24c
c = 3
So, the speed of the current is 3 mph.
To find the speed of the current, we can set up an equation based on the given information.
Let's assume the speed of the current is represented by 'c' mph.
When the boat is moving downstream (in the same direction as the current), the effective speed of the boat is increased by the speed of the current. So, the boat's speed downstream would be 18 mph + c mph.
Similarly, when the boat is moving upstream (against the current), the effective speed of the boat is decreased by the speed of the current. So, the boat's speed upstream would be 18 mph - c mph.
Now, we are given that the boat travels 14 miles downstream in the same amount of time it takes to travel 10 miles upstream.
To determine the time taken for each journey, we can use the formula:
Time = Distance / Speed
So, we can set up the following equation based on the given information:
14 / (18 + c) = 10 / (18 - c)
To solve this equation, we can cross multiply:
14 * (18 - c) = 10 * (18 + c)
Simplifying the equation further, we get:
252 - 14c = 180 + 10c
Rearranging and combining like terms, we have:
14c + 10c = 252 - 180
24c = 72
Dividing both sides by 24, we find:
c = 3
Therefore, the speed of the current is 3 mph.