Question

A canoeist paddles 21 km downstream in 3h. The return trip takes 1.2 h longer. What is the rate of the current?

Answer 1

You have to know two things: The area of the flow and the speed of the flow. To get the area you have to measure the depth and width of the river at a particular cross-section perpendicular to the flow direction.

Answer 2

Do you know rate * times = distance or velocity * time = distance or speed * time= distance
(All mean the same thing)

Let's use rate. The rate of the paddler is P (for paddler) in km/hr (kph) in still water
Call the rate of the current C (C for current)
if she is going with the current we add in how fast the current is:

downstream the rate is P+C
going upstream the paddler goes slower because the current subtracts from her rate,
upstream the rate is P-C

now use rate * time = distance

can you write down the equation when going downstream ?

Answer 3

21km/3h?

Answer 4

yes, but that is not an equation. I meant like this:

DOWNSTREAM:
rate * time = distance

replace rate with (P+C) (that is the rate going downstream, though we don't know P or C)
replace time with 3 hours
replace distance with 21 km

we get
(P+C) * 3 hrs = 21 km

that I is what I mean by "write the equation"

can you write down the equation for going upstream?

Answer 5

Oh sorry , upstream = (P-C)4.2hrs=21km

Answer 6

yes, looks good. now we use algebra to solve for C to answer the question
What is the rate of the current?

so we have
3(P+C) =21
4.2(P-C)= 21

I would simplify both equations. In the first, divide both sides by 3 (like you posted up above) . In the 2nd, divide both sides by 4.2

what are the equations now?

Answer 7

(P+C)=7km/h
(P-C)=5km/h

Answer 8

to find C, I would subtract: top equation minus bottom equation. Can you finish ?

Answer 9

2P=12km/h
P=6km/hr

6km/hr+C=7km/hr
C=1km/h

Answer 10

Yes if you added the 2 equations you would get
(P+C)=7km/h
(P-C)=5km/h

2P +C -C = 12
2P= 12
P= 6

and then you can find C

you could also subtract equations like this

(P+C)=7km/h
-(P-C)=-5km/h (put a minus sign in front of both sides)
P+C-(P-C) = 7 - 5
P+C-P +C = 2
2C= 2
C=1 km/hr

Answer 11

Thank you!

Answer 12

yw