Question

Evelyn can row 48 miles downstream in eight hours. It takes her 12 hours to row the same distance upstream. Find the rate she rows in still water and the rate of the current.

Answer 1

Let's define:

Se = speed (or rate at which she rows) of Evelyn in still water.

Sr = speed of the river water (or the speed of the current).

When she travels downstream, her speed will be equal to her speed in still water plus the speed in the river, and we know that she can row 48 miles in 8 hours.

If we use the relationship:

Speed*time = distance

we can write:

(Se + Sr)*8h = 48mi.

When she travels upstream, her speed will be equal to her speed in still water minus the speed of the river. In this case, we know that she needs 12 hours to row 48 miles, then we have the equation:

(Se - Sr)*12h = 48mi

Then we have a system of equations:

(Se + Sr)*8h = 48mi

(Se - Sr)*12h = 48mi

To solve this, we first need to isolate one of the variables in one of the equations,

Let's isolate Se in the second equation:

(Se - Sr)*12h = 48mi

(Se - Sr) = 48mi/12h = 4 mi/h

Se = 4mi/h + Sr

Now we can replace this in the other equation, to get:

(Se + Sr)*8h = 48mi

(4mi/h + Sr + Sr) = 48mi/8h = 6mi/h

4mi/h + 2*Sr = 6mi/h

2*Sr = 6mi/h - 4mi/h = 2mi/h

Sr = (2mi/h)/2 = 1mi/h

Then the speed of the river is 1 miler per hour.

And we can use the equation Se = 4mi/h + Sr to find the speed of Evelyn in still water:

Se = 4mi/h + 1mi/h = 5mi/h

The speed of Evelyn in still water is 5mi/h.