It takes 3 hours to paddle a kayak 12 miles downstream and 4 hours for the return trip upatream. find the rate of the kayak in still water.

The speed of Kayak in still water is 3.5 miles per hour .

Step-by-step explanation:

Given as :

The distance cover in downstream = 12 miles

The time taken to paddle downstream = 3 hours

The distance cover in upstream = 12 miles

The time taken to paddle upstream = 4 hours

Let the speed of Kayak in still water = x mph

And The speed of current = y mph

Now, Speed =

For downstream

x + y =

Or, x + y =

∴ x + y = 4  miles per hour           ............A

For upstream

x - y =  

or, x - y =  

∴ x - y = 3  miles per hour             .........B

solving eq  A and B

So, ( x + y ) + ( x - y ) = 4 + 3

Or, ( x + x ) + ( y - y ) = 7

Or, 2 x + 0 = 7

∴  x =

I.e x = 3.5 mph

so, speed of Kayak = x = 3.5 mph

Hence The speed of Kayak in still water is 3.5 miles per hour . Answer