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.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

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step-by-step explanation: