The rate of the kayak in still water is 3.5 mph
Given that It takes 3 hours to paddle a kayak 12 miles downstream
Distance covered in downstream = 12 miles
Time taken to cover downstream = 3 hours
Also given that it takes 4 hours for the return trip upstream
Distance covered in upstream = 12 miles
Time taken to cover upstream = 4 hours
Formula to remember:
If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then: Speed downstream = (u + v) km/hr and Speed upstream = (u - v) km/hr
Let the speed of Kayak in still water = x mph
And The speed of current = y mph
For downstream:
Speed downstream = x + y
We know that [tex]speed = \frac{distance}{time}[/tex]
[tex]\frac{distance}{time} = x + y[/tex]
[tex]x + y = \frac{12}{3}[/tex]
x + y = 4 ------ eqn 1
For upstream:
Speed upstream = x - y
[tex]\frac{12}{4} = x - y[/tex]
x - y = 3 -------- eqn 2
Now let us eqn 1 and eqn 2
Add eqn 1 and eqn 2
x + y + x - y = 4 + 3
2x = 7
x = 3.5
speed of Kayak in still water = x mph = 3.5 mph
