Question 439565
Draw a figure as follows:

Draw a horizontal line representing the shoreline. Pick a point on this line and label it A. From A move up two units (where a unit is any convenient distance) and mark this point as R. This is where the man in the rowboat is located at the beginning. From A, move six units along the "shoreline" and mark this point as B. Pick some point between A and B and label this point as P. Finally, draw line segment PR.

{{{AR = 2 miles}}}
{{{AB = 6 miles}}}
{{{PB = x miles}}}

so

{{{AP = AB - PB = (6-x) ml}}}

From Pythagorean Theorem,

{{{PR^2 = AR^2 + AP^2}}}

= {{{4 + (6-x)^2}}}

= {{{40 - 12x + x^2}}}

so

{{{PR = sqrt(40 - 12x + x^2)miles }}}

The time it will take to row this distance is

{{{sqrt(40 - 12x + x^2) miles / (3mi / hr) = (sqrt(40 - 12x + x^2)/3) hr}}}

The time it will take to walk from P to B is

{{{x mil / (5mil / hr) = (x/5) hr}}}

So the total time {{{T}}} in hours to reach the house is given by

{{{T =sqrt(40 - 12x + x^2)/3 + (x/5)}}}