The current of a river is 6 miles per hour. A boat travels to a point 24 miles upstream and back again in 3 hours. What is the speed of the boat to the nearest tenth in water without a current?

Answer 1

Hi Luis, let x represent the speed of the boat. Then the speed of the boat against the river will be x - 6 and the speed of the boat with the river will be x + 6.

Using the formula, D(istance) = R(ate) * T(ime), we can set up an equation representing the time of travel.

24 / (x + 6) represents the time with the river and 24 / (x - 6) represents the time against the river. These two values added together represents the time of travel, or 3 hours.

24 / (x + 6) + 24 / (x - 6) = 3

Multiply the entire equation by (x + 6) * (x - 6) to clear the fractions:

24 * (x - 6) + 24 * (x + 6) = 3 * (x - 6) * (x + 6)

Clear parentheses:

24x - 144 + 24x + 144 = 3 * (x² - 36)

Combine terms:

48x = 3x² - 108

Subtract 48 from both sides:

3x² - 48x - 108 = 0

Divide entire equation by 3:

x² - 16x - 36 = 0

Factor:

(x + 2) * (x - 18) = 0

Use the zero product rule:

x + 2 = 0

x = -2, we can discard this solution because the rate of the boat cannot be negative.

x - 18 = 0

x = 18

The rate of the boat in water without a current is 18 miles per hour.

Questions?