Question18. Two friends can paddle a canoe at a rate of $6 \mathrm{~km} / \mathrm{h}$ in still water. It takes them 1 h to paddle 2 km up a river and back again. Find the speed of the current.

Studdy Solution
Solve the equation.
First, find a common denominator and combine the fractions:
$$\frac{2(6 + c) + 2(6 - c)}{(6 - c)(6 + c)} = 1$$
Simplify the numerator:
$$\frac{12 + 2c + 12 - 2c}{36 - c^2} = 1$$
$$\frac{24}{36 - c^2} = 1$$
Cross-multiply to solve for $c^2$:
$$24 = 36 - c^2$$
Rearrange the equation:
$$c^2 = 36 - 24$$
$$c^2 = 12$$
Take the square root of both sides:
$$c = \sqrt{12}$$
$$c = 2\sqrt{3}$$
The speed of the current is $2\sqrt{3} \, \text{km/h}$.