SOLUTION: Hello! A man in a rowboat that is 2 miles from the nearest point A on a straight shoreline wishes to reach a house located at a point B that is 6 miles farther down the shoreli

Algebra ->  Functions -> SOLUTION: Hello! A man in a rowboat that is 2 miles from the nearest point A on a straight shoreline wishes to reach a house located at a point B that is 6 miles farther down the shoreli      Log On


   

Question 439565: Hello!
A man in a rowboat that is 2 miles from the nearest point A on a straight shoreline wishes to reach a house located at a point B that is 6 miles farther down the shoreline. He plans to row to a point P that is between A & B and is x miles from the house, and then he will walk the remainder of the distance. Suppose he can row at a rate of 3mi/hr and can walk at the rate of 5mi/hr. If T is the total time required to reach the house, express T as a function of x.
Thanks
Mak
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
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+=+%286-x%29+ml
From Pythagorean Theorem,
PR%5E2+=+AR%5E2+%2B+AP%5E2
= 4+%2B+%286-x%29%5E2
= 40+-+12x+%2B+x%5E2
so
PR+=+sqrt%2840+-+12x+%2B+x%5E2%29miles+
The time it will take to row this distance is

The time it will take to walk from P to B is
x+mil+%2F+%285mil+%2F+hr%29+=+%28x%2F5%29+hr
So the total time T in hours to reach the house is given by
T+=sqrt%2840+-+12x+%2B+x%5E2%29%2F3+%2B+%28x%2F5%29