3. Yves Trough, a French Canadian fur trader, took 2 hours to paddle his canoe 24 km downstream to the Hudson's Bay trading post.The return trip against the current took 3 hours. Find the speed of the canoe in still water and the speed of the current.

Let 'c' be the speed of the canoe in still water (km/h) and 'w' be the speed of the current (km/h).<br /><br />**Downstream:**<br /><br />* The speed of the canoe going downstream is the sum of the canoe's speed and the current's speed (c + w).<br />* The distance traveled downstream is 24 km.<br />* The time taken downstream is 2 hours.<br />* We can use the formula: distance = speed × time<br /><br />Therefore, 24 = (c + w) × 2 ---> Equation (1)<br /><br />**Upstream:**<br /><br />* The speed of the canoe going upstream is the difference between the canoe's speed and the current's speed (c - w).<br />* The distance traveled upstream is also 24 km (same distance back).<br />* The time taken upstream is 4 hours.<br />* Using the same formula: distance = speed × time<br /><br />Therefore, 24 = (c - w) × 4 ---> Equation (2)<br /><br />Now we have a system of two equations with two variables:<br /><br />Equation (1): 2c + 2w = 24<br />Equation (2): 4c - 4w = 24<br /><br />We can simplify these equations:<br /><br />Equation (1): c + w = 12 (Divide both sides by 2)<br />Equation (2): c - w = 6 (Divide both sides by 4)<br /><br />Now we can solve for 'c' and 'w' using either substitution or elimination. Here's the elimination method:<br /><br />Add Equation (1) and Equation (2):<br /><br />(c + w) + (c - w) = 12 + 6<br />2c = 18<br />c = 9<br /><br />Now substitute the value of 'c' (9) back into either Equation (1) or (2). Let's use Equation (1):<br /><br />9 + w = 12<br />w = 12 - 9<br />w = 3<br /><br />Therefore, the speed of the canoe in still water is $\boxed{9}$ km/h, and the speed of the current is $\boxed{3}$ km/h.<br />