A boat can travel 24 mph in still water. If it travels 186 miles with the current in the same length of time it travels 102 miles against the current, what is the speed of the current?

since time = distance/speed,

186/(24+x) = 102/(24-x)

To find the speed of the current, let's assume "x" as the speed of the current.

When the boat is traveling with the current, the effective speed will be the sum of the boat's speed in still water and the speed of the current. So the speed with the current will be: 24 mph + x mph.

When the boat is traveling against the current, the effective speed will be the difference between the boat's speed in still water and the speed of the current. So the speed against the current will be: 24 mph - x mph.

Now, to solve the problem, we need to set up an equation using the given information. The equation will be based on the fact that the time taken to travel a certain distance is equal, regardless of whether the boat is traveling with or against the current.

The time taken to travel a certain distance can be calculated using the formula: time = distance/speed.

Let's set up the equation for both scenarios:

For traveling with the current: time = distance/speed = 186 miles / (24 mph + x mph)

For traveling against the current: time = distance/speed = 102 miles / (24 mph - x mph)

Since the times are equal in both scenarios, we can set up the equation:

186/(24+x) = 102/(24-x)

Now, we can solve this equation for x, which represents the speed of the current.

To do that, we can cross-multiply:

186*(24-x) = 102*(24+x)

Simplifying,

4464 - 186x = 2448 + 102x

Next, rearrange the equation:

102x + 186x = 4464 - 2448

288x = 2016

x = 2016/288

x ≈ 7

Therefore, the speed of the current is approximately 7 mph.