A camper paddles a canoe 2 miles downstream in a river that has a 2-mile-per-hour current. To return to camp, the canoeist travels upstream on a different branch of the river. It is 4 miles long and has a 1-mile-per-hour current. The total trip (both ways) takes 3 hours. Find the average speed of the canoe in still water. Time = distance/rate

The average speed of the canoe in still water is 2.56 miles/hour.

Step-by-step explanation:

Step 1:

According to the given information:

Canoe speed downstream = 2 miles/hour

Canoe speed upstream = 1 mile/hour

Distance with downstream = 2 miles

Distance with upstream = 4 miles

Let the average speed be 'x'

Then, Speed with current = x+2 miles/hour

And, speed against current = x-1 miles/hour

Total time = 3 hours

Therefore,

time with current (downstream) = 2 / x + 2

time against current (upstream) = 4 / x - 1

Total time = (2 / x + 2) + (4 / x - 1)

Step 2:

Now, put the value of total time and solve:

Total time = (2 / x + 2) + (4 / x - 1)

3 = (2 / x + 2) + (4 / x - 1)

3 = (2 (x - 1) + 4 (x + 2)) / (x + 2) (x - 1)

3 = (2x - 2 + 4x + 8) / (x² + x - 2)

3 (x² + x - 2) = 6x + 6

x² - x - 4 = 0

Step 3:

Solving the quadratic equation:

x = ( - (-1) ±√[ (-1) ² - 4 (1) (-4) ]) / 2 (1)

x = 1 ± √ (17) / 2

⇒ x₁ = 2.56, x₂ = - 1.56

Step 4:

Since an average speed cannot be negative, the answer will be x₁ = 2.56.

Therefore, the average speed of the canoe in still water is 2.56 miles/hour.