It takes a boat 2 hours to travel 26 miles downstream and 4 hours to travel 28 miles upstream.
So???? I don't see a question here.
To solve this problem, we need to consider the concept of relative motion. When a boat is moving downstream (along the direction of the current), the effective speed of the boat increases. Conversely, when the boat is moving upstream (against the direction of the current), the effective speed decreases.
Let's start by assigning variables to the different quantities involved. Let's say:
- The speed of the boat in still water is "b" (in miles per hour).
- The speed of the current is "c" (in miles per hour).
Now, let's calculate the boat's effective speed when traveling downstream and upstream.
Downstream:
The effective speed of the boat when traveling downstream is given by the sum of the boat's speed in still water (b) and the speed of the current (c):
Speed downstream = b + c
Using the given information, we know that it takes 2 hours for the boat to travel 26 miles downstream. So we can set up the equation:
Speed downstream * Time = Distance
(b + c) * 2 = 26
Upstream:
The effective speed of the boat when traveling upstream is given by the difference between the boat's speed in still water (b) and the speed of the current (c):
Speed upstream = b - c
Using the given information, we know that it takes 4 hours for the boat to travel 28 miles upstream. So we can set up the equation:
Speed upstream * Time = Distance
(b - c) * 4 = 28
Now we have a system of two equations:
2(b + c) = 26 (Equation 1)
4(b - c) = 28 (Equation 2)
We can solve this system of equations simultaneously to find the values of b and c.
To solve Equation 1, we can divide both sides of the equation by 2:
b + c = 13 (Equation 3)
To solve Equation 2, we can divide both sides of the equation by 4:
b - c = 7 (Equation 4)
Now we can solve Equations 3 and 4 simultaneously. One way to solve this is by adding Equations 3 and 4:
(b + c) + (b - c) = 13 + 7
2b = 20
Dividing both sides of the equation by 2, we find that:
b = 10
Now we can substitute the value of b back into Equation 4 (b - c = 7) to find the value of c:
10 - c = 7
c = 10 - 7
c = 3
Therefore, the speed of the boat in still water is 10 miles per hour, and the speed of the current is 3 miles per hour.