A riverboat cruise line has a boat that can travel 76 mi downstream in the same time that it takes to travel 52 mi upstream. The speed of the current in the river is 1.5 mph. Find the speed of the boat in still water.

speed of boat in still water ---- x mph

speed against current = x-1.5
speed downstream = x+1.5

time to go 75 miles downstream = 75/(x+1.5)
time to go 52 miles upstream = 52/(x-1.5)

so 75/(x+1.5) = 52/(x-1.5)
cross-multiply and solve for x

so answer is 8?

76x - 114 = 52x + 78
24x = 192
x = 8

To find the speed of the boat in still water, we can let the speed of the boat be represented by "b" and the speed of the current be represented by "c".

When the boat travels downstream with the current, the effective speed is the sum of the speed of the boat and the speed of the current: b + c.

When the boat travels upstream against the current, the effective speed is the difference between the speed of the boat and the speed of the current: b - c.

We are given that the boat can travel 76 miles downstream in the same time it takes to travel 52 miles upstream.

Using the formula Time = Distance / Speed, we can set up the following equation:

76 / (b + c) = 52 / (b - c).

We can start by cross-multiplying and then simplifying the equation:

76(b - c) = 52(b + c).

Expanding both sides of the equation:

76b - 76c = 52b + 52c.

Combining like terms:

24b = 128c.

Now, we can solve for b (the speed of the boat in still water) by dividing both sides of the equation by 24:

b = (128c) / 24.

Given that the speed of the current is 1.5 mph (c = 1.5), we can substitute this value into the equation to find the speed of the boat in still water:

b = (128 * 1.5) / 24.

b = 8 mph.

Therefore, the speed of the boat in still water is 8 mph.