Acamper 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.

answer

explanation

the area of a circle is calculated using the formula

or

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

we substitute the diameter into the formula to get:

this is the exact value for the area of the circle.

the correct answer is a

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.