it takes 3.2 hours to canoe 12 miles downstream and 4.8 hours to paddle upstream, what is average paddling speed in still water and the current of the river

Question

This is a system of equations and it is really hard for me.

Answer 1

Let Vs be the average speed in still water
Let Vc be the average speed of the current
Average speed = Total distance
Total time
Downstream
Net average speed = Vs + Vc
Average speed = 12
                         3.2
So (I) 12 = Vs + Vc
         3.2

Upstream
Net average speed = Vs - Vc
So (ii) 12 = Vs - Vc
         4.8
Adding (i) and (ii)
12 = Vs + Vc
3.2

12 = Vs - Vc
4.8
12 + 12 = 2Vs
4.8   3.2
2.5 + 3.75 = 2Vs
6.25 = 2Vs
3. 125 or 3 1/8 = Vs

Substituting for Vs in (i) 
3.75 = 3.125 + Vc
3.75 - 3.125 = Vc
0.625 (5/8) = Vc
Answer Average speed in still water is 3.125 or 3 1/8 mph
Average speed of the stream is 0.625 or 5/8 mph

 

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Answer 2

The speed of canoeing downstream is 12mi/3.2h = 3.75 mi/h. For upstream, it is 12/4.8 mi/h =2.5 mi/h.

 

Let's call the paddling speed s, and the current speed c. When paddling downstream, you're going with the current, so your speed is the sum of the paddling speed and the current, that is,

 

s + c = 3.75 mi/h        (Eq. 1)

 

When paddiling upstream, conversely your speed will be reduced buy the current, so your total speed is your paddling speed minus the current,

 

s - c = 2.5 mi/h          (Eq. 2)

 

Adding eq. 1 and eq. 2 gives:

 

(Eq. 1) + (Eq. 2):

 

2s = 6.25 mi/h

 

and now we divide

by 2 to get the answer for your paddling speed, s = 3.125 mi/h. You can substitute this back into eq. 1 or eq. 2 to get the answer for the current speed c.

 

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