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The rate of the kayak in still water is 3.5 mph
<h3><u>Solution:</u></h3>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
<em><u>Formula to remember:</u></em>
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
x + y = 4 ------ eqn 1
<em><u>For upstream:</u></em>
Speed upstream = x - y
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