Steve's boat will go 14 miles per hour in still water. If he can go 13 miles downstream in the same amount of time as it takes to go 10 miles upstream, then what is the speed of the current? (Please round your answer to one decimal place.)
To find the speed of the current, we can use the concept of relative speed. When the boat is going downstream, it gets an additional push from the current, while when it is going upstream, it faces resistance against the current.
Let's assume the speed of the current is "C" miles per hour.
When the boat is going downstream, its effective speed will be the sum of its speed in still water and the speed of the current. So the effective speed downstream becomes (14 + C) miles per hour.
Similarly, when the boat is going upstream, its effective speed will be the difference between its speed in still water and the speed of the current. So the effective speed upstream becomes (14 - C) miles per hour.
We are given that the time it takes to go 13 miles downstream is the same as the time it takes to go 10 miles upstream.
Using the formula time = distance / speed, we can set up the following equation:
13 / (14 + C) = 10 / (14 - C)
To solve for C, let's cross-multiply and simplify the equation:
13(14 - C) = 10(14 + C)
182 - 13C = 140 + 10C
Combine like terms:
-13C - 10C = 140 - 182
-23C = -42
Divide both sides by -23:
C = (-42) / (-23)
C ≈ 1.83
Therefore, the speed of the current is approximately 1.8 miles per hour (rounded to one decimal place).