Question

With the current, you can canoe 72 miles in 4 hours. Against the same current, you can canoe only 3/4 of this distance in 6 hours. Find your rate in still water and the rate of the current.

Answer 1

The rate in still water is 13.5 miles per hour and the rate of the current is 4.5 miles per hour.

Explanation:

The velocity of an object is equal to the displacement divided by the time:

`v=(d)/(t)`

Going with the current the velocity in miles per hour is:

`v_1=(72)/(4)=18`

Going against the current, 3/4 of 72 miles is 54 miles, then the velocity in miles per hour is:

`v_2=(54)/(6)=9`

The velocity of going with the current is the sum of the rate of being still(
`s`) and the rate of the current(
`c`). And the velocity of going against is the difference between the two rates so:

`s+c=18`

`s-c=9`

Adding the equation to solve for
`s`:

`\frac{{{s+c=18} \atop {s-c=9}}}{2s \ =27}`

`s=13.5`

Substituting
`s` in one equation to find
`c`:

`s+c=18  \\ 13.5+c=18 \\ c=18-13.5 \\c=4.5`

The rate in still water is 13.5 miles per hour and the rate of the current is 4.5 miles per hour.