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

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) (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.

From Pythagorean Theorem,

=
=
so

The time it will take to row this distance is

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

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

RELATED QUESTIONS
A man in a rowboat that is a = 4 miles from the nearest point A on a straight shoreline... (answered by Theo)

In a diagram, a man is in a rowboat at point A, which is located 3 miles from point B,... (answered by ankor@dixie-net.com)

Jane is 2 miles offshore in a boat and wishes to reach a coastal village 6 miles down a... (answered by ankor@dixie-net.com,Alan3354)

I've been working on this problem and can only come up with an estimation, with no way of (answered by ankor@dixie-net.com)

A boardwalk is parallel to and 210 ft inland from a straight shoreline. A man is standing (answered by ankor@dixie-net.com)

A boardwalk is parallel to and 210 ft inland from a straight shoreline. A sandy beach... (answered by ankor@dixie-net.com)

A boardwalk is parallel to and 210 ft inland from a straight shoreline. A sandy beach... (answered by solver91311,ankor@dixie-net.com)

The Sea Kayak Problem: Brooke is located 5 miles out from the nearest point A along a... (answered by ikleyn)

A ship is anchored 9 miles from the nearest point of a straight beach. A man in the ship... (answered by ankor@dixie-net.com)