A person in a rowboat 2 miles from the nearest point P on a straight shoreline wishes to reach a house 6 miles down the shoreline from P.If the...

The nearest distance of the person  to the spot P on the
shore = 2miles.

Let starting point of the person to row the
boat be S. Then SP = 2.

Let the house be at the spot H on
the bank of the river.

Then SP = 2, SH = 6
miles.

Therefore PSH form a right angled triangle with
right angle at S.

Therefore PS^2+SH^2 = PH^2 by Pyhagoras
theorem.

2^2+6^2 = PH^2.

Or
PH^2 = 2^2+6^2 = 4+36 = 40

Therefore PH = sqrt(40) = 6.3246
miles.

Therefore the time required to row SH = 6 miles at
the rate of 3mph = 6/3 = 2 hours.

The time required to walk
the distance of PH = 6.3246 miles at the rate of 5 miles per hour = 6.3246/5 = 1.2649
hours = 1 hour 15.9 minutes nealy.

So the least time to
reach is the option of walking.