Answer:
Explanation:
Let's use the following variables:
Let b be the speed of the boat in calm water in miles per hour.
Let c be the speed of the current in miles per hour.
When the woman paddles downstream with the current, her speed is b + c miles per hour. When she paddles upstream against the current, her speed is b - c miles per hour. We can use the formula:
distance = rate × time
to write two equations based on the information given:
Downstream: 28 = (b + c) × 2
Upstream: 28 = (b - c) × 7
Simplifying these equations, we get:
2b + 2c = 28
7b - 7c = 28
We now have a system of two linear equations with two variables. We can solve for b and c using any method of solving systems of equations. For example, we can use elimination to eliminate one of the variables. Multiplying the first equation by 7 and the second equation by 2, we get:
14b + 14c = 196
14b - 14c = 56
Adding the two equations, we get:
28b = 252
b = 9
Substituting b = 9 into one of the original equations, we can solve for c:
2(9) + 2c = 28
2c = 10
c = 5
Therefore, the speed of the boat in calm water is 9 miles per hour, and the speed of the current is 5 miles per hour.