Question

It takes 2 hours for Ian to travel 16 miles upstream in his boat, and it takes 3 hours to travel 36 miles downstream. Which system of linear equations can be used to find the speed of the boat (b) in still water and the rate of the current (c)?

Answer 1

The system of equations to find the speed of the boat in still water (b) and the rate of the current (c) is:

Equation 1: 8b - 4c = 16 (representing upstream travel)

Equation 2: 12b + 6c = 36 (representing downstream travel)

Step-by-step explanation:

Let b be the speed of the boat in still water and c be the rate of the current.

Upstream, the boat's speed is b - c (current opposes the boat). In 2 hours, it travels 16 miles, so 2(b - c) = 16.

Downstream, the boat's speed is b + c (current aids the boat). In 3 hours, it travels 36 miles, so 3(b + c) = 36.

Simplify both equations: Equation 1: 8b - 4c = 16 and Equation 2: 12b + 6c = 36.

These two equations represent the system that can be used to solve for b and c.

Answer 2

The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour.

Step-by-step explanation:

Given,

In upstream it takes 2 hours to travel 16 km

In downstream it takes 3 hours to travel 36 km

To find the speed of the boat (b) in still water and the rate of the current (c)

Formula

Distance = Speed × Time

According to the problem,

b-c =
`(16)/(2) = 8` ------ (1)

b+c =
`(36)/(3)` = 12 ------- (2)

Adding (1) and (2) we get,

b-c+b+c = 8+12

or, 2b = 20

or, b = 10

Subtracting (1) from (2) we get,

b+c-b+c = 12-8

or, 2c = 4

or, c = 2

Hence,

The speed of the boat (b) in still water is 10 miles/hour and the rate of the current (c) is 8 miles/hour.