Answer:
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.
