Question 204259
Use the distance formula:
{{{d = r*t}}} where: d = distance trveled, r = rate(speed), and t = time of travel.
For the trip upstream (against the current of 2mph), d = 14mi. and r = speed of the boat, so you can write:
{{{14 = (r-2)*t}}} The speed of the current is subtracted from the speed of the boat going upstream.
For the trip downstream (with the current of 2mph), d = 21mi, and r = the speed of the boat, so you can write:
{{{21 = (r+2)*t}}} The time, t, is the same in both cases, so we solve both equations for t and set them equal to each other.
Upstream trip:
{{{t = 14/(r-2)}}}
Downstream trip:
{{{t = 21/(r+2)}}} Set these equal to each other.
{{{14/(r-2) = 21/(r+2)}}} Solve for r, the speed of the boat in still water. Cross multiply.
{{{14(r+2) = 21(r-2)}}} Simplify.
{{{14r+28 = 21r-42}}} Subtract 14r from both sides.
{{{28 = 7r-42}}} Add 42 to both sides.
{{{70 = 7r}}} Finally, divide both sides by 7.
{{{r = 10}}}
The speed of the boat in still water is 10mph.