A boat can go 20 miles against a current in the same times that it can go 60 miles with the current. The current is 4 miles per hour. Find the speed of the boat with no current.

d1 = (Vb-4)t = 20

Eq1: Vb*t - 4t = 20

d2 = (Vb+4)t = 60
Eq2: Vb*t + 4t = 60

Multiply Eq1 by -1:
-Vb*t + 4t = -20
+Vb*t + 4t = 60
Sum:0 + 8t = 40
t = 5 h.

In Eq1, replace t with 5:
Vb*5 - 4*5 = 20
5Vb = 40
Vb = 8 mi/h = Velocity of the boat.

To find the speed of the boat with no current, we can use the formula:

Boat's speed with no current = Boat's speed with current - Current's speed.

Let's assign variables to the unknown quantities:
Let B be the speed of the boat with no current (in miles per hour).
Let C be the speed of the current (in miles per hour).

Given:
The boat can go 20 miles against the current in the same time it can go 60 miles with the current.
The current speed is 4 miles per hour.

First, let's find the time it takes to travel the given distances.

Against the current:
Distance = 20 miles
Relative speed = Boat's speed with no current - Current's speed = B - C
Time = Distance / Relative speed = 20 / (B - C) hours

With the current:
Distance = 60 miles
Relative speed = Boat's speed with no current + Current's speed = B + C
Time = Distance / Relative speed = 60 / (B + C) hours

According to the given information, both times are equal. Therefore, we can write an equation:

20 / (B - C) = 60 / (B + C)

To solve for B, we can cross multiply and solve the resulting equation.

20(B + C) = 60(B - C)
20B + 20C = 60B - 60C
80C = 40B
2C = B

Since C = 4 (as given), we can substitute it into the equation above:

2(4) = B
8 = B

Therefore, the speed of the boat with no current is 8 miles per hour.