Question

A woman paddling a canoe downstream with the river current travels 28 miles in 2 hours. On the return trip, she paddles the same distance upstream against the river current in 7 hours. Write and solve a system of two linear equations to determine the rate of the boat in calm water and the rate of the current, both in miles per hour.

calm water

Answer 1

What the person said above me

Answer 2

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.