A canoeist paddled downstream for 4 hours with a 6km/h current to reach a campsite. The return trip against the current took 10 hours. Find the speed of the canoe in still water.

Answer 1

Vc = velocity of canoe

Vw = velocity of water

d = t*v

Downstream: d = 4(Vc + Vw)

Upstream: d = 10(Vc - Vw)

d is the same so set them =, and plug in Vw

4(Vc + 6) = 10(Vc - 6)

Vc = 14

Answer 2

Distance = (Rate)(Time)

Let x = speed of canoe in still water

Then, speed with current = x+6 and speed against current = x-6

Distance upstream = Distance downstream

4(x + 6) = 10(x - 6)

4x + 24 = 10x - 60

6x = 84

x = 14 km per hour

Answer 3

Let x be the speed of the canoe in still water in km/hour. Therefore, the speed of the canoe going downstream is x+6 km/hour, and going back upstream is x-6 km/hour. Let d be the distance in km to the campsite. Recall that dividing the distance by the speed gives the travel time of the journey. Therefore, according to the problem,

Downstream - 4 = d/(x+6)

Upstream - 10=d/(x-6)

Rearrange the equations to get

4(x+6) = d and

10(x-6) = d

Since the two distances are the same, they can be set equal to each other, so

4(x+6)=10(x-6)

Expand both sides to get

4x+24 = 10x - 60

Rearrange to get

24+60 = 10x-4x

Simplify to get 84= 6x

Divide both sides by 6 to get the final answer of x= 14 (remember, x was defined as km/hr)

Final answer - speed of canoe in still water is 14 km/hour

Answer 4

Let V = speed of canoe in still water.

Let D = Distance traveled one way.

Rate * Time = Distance

Rowing downstream at a speed of V + 6 km/h for 4 hours gives a total one-way distance of 4(V+6).

Rowing upstream at a speed of V - 6 km/h for 10 hours gives a total one-way distance of 10(V-6).

Equating these distances yield:

4(V+6) = 10(V-6)

4V + 24 = 10V - 60

24 + 60 = 10V - 4V

84 = 6V

V = 14 km/h, ans.

Check:

4(14+6) = 10(14-6)

4(20) = 10(8)

80 = 80