Question

HELP - I do not understand word problems.
**Use two variables to setup & solve**
Kayaking: A kayaking group with a guide travels 16 miles downstream, stops for a meal, and then travels 16miles upstream. The speed of the current re
mains constant throughout the trip. Find the speed of the kayak in still water.
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It then gives a table where it states:
Leave @ 10 am
Stop for meal @ 12pm
Return @ 1pm
Finish @ 5pm

Let x=speed of kayak in still water
Let y=speed of current

Answer 1

Basically, we apply the formula
\[\large speed = \frac{distnace}{time}\]
Note that the distance travelled is the same for travelling downstream and upstream

Consider travelling downstream
Speed = x+y
Time = 2 hours
Distance travelled = 16miles = 2(x+y)

Consider travelling downstream
Speed = x-y
Time = 4 hours
Distance travelled = 16miles = 4(x-y)

So,
16 = 2(x+y) => 8 = x+y -(1)
16 = 4(x-y) => 4 = x-y -(2)

(1) + (2)
2x = 12
x = 6 miles/hour

4 = x-y
4 = 6 -y
y = ...?

Not sure if it is correct...

Answer 2

thank you - i checked the work and it's correct I get it now