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.
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To find the speed of the boat with no current, we can use the concept of relative speed.
Let's assume that the speed of the boat with no current is x miles per hour.
When the boat goes against the current, the effective speed is reduced by the speed of the current. So, the speed of the boat against the current is (x - 4) miles per hour.
Similarly, when the boat goes with the current, the effective speed is increased by the speed of the current. So, the speed of the boat with the current is (x + 4) miles per hour.
Now, let's use the formula: time = distance / speed.
According to the given information, the boat takes the same amount of time to travel 20 miles against the current and 60 miles with the current. Therefore, we can set up the following equation:
20 / (x - 4) = 60 / (x + 4)
To solve this equation, we can cross multiply:
20(x + 4) = 60(x - 4)
Simplifying this equation:
20x + 80 = 60x - 240
Rearranging the terms:
60x - 20x = 240 + 80
40x = 320
Dividing both sides by 40:
x = 8
Therefore, the speed of the boat with no current is 8 miles per hour.