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.

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.