SOLUTION: A boy is at a point A on a straight river. He can row downstream at a rate which is 2 miles an hour faster than he can run. If he rows downstream to a point B, which is 4 miles bel

Question 1196590: A boy is at a point A on a straight river. He can row downstream at a rate which is 2 miles an hour faster than he can run. If he rows downstream to a point B, which is 4 miles below A, and runs, in a direction perpendicular to the river, to a point C, three miles from B, it takes him ten minutes longer than it does to run directly from A to C. How fast can he run?
Answer by ikleyn(52754) (Show Source): You can put this solution on YOUR website!
.
A boy is at a point A on a straight river.
He can row downstream at a rate which is 2 miles an hour faster than he can run.
If he rows downstream to a point B, which is 4 miles below A, and runs,
in a direction perpendicular to the river, to a point C, three miles from B,
it takes him ten minutes longer than it does to run directly from A to C.
How fast can he run?
~~~~~~~~~~~~~

Notice that ABC is a right angled triangle with right angle at B.
The hypotenuse AC is 5 miles long (the legs AB and BC are 4 miles and 3 miles, respectively).


Let x be his rate running, in miles per hour.

Then his rate rowing downstream is (x+2) miles, according to the problem.


His time running AC is    hours.

His time rowing from A to B and then running from B to C is   +   hours.


The time equation is 

     +  -  = 1/6  of an hour   (i.e. 10 minutes).    (1)


         +------------------------------------------+
         |   At this point, the setup is complete.  |
         +------------------------------------------+


To solve equation, multiply both sides by 6x*(x+2).  You will get

    24x + 18(x+2) - 30(x+2)    = x*(x+2)

    24x + 18x + 36 - 30x  - 60 = x^2 + 2x

    12x - 24                   = x^2 + 2x

    x^2 - 10x + 24 = 0

    (x-6)*(x-4) = 0


It gives two roots:  x= 6 mph  and  x= 4 mph.


We keep both roots x = 6 mph and x = 4 mph as possible answers.


Let check by substituting this value into equation (1)


    x = 6:     +  -  =  =  =  =   (correct),  


    x = 4:     +  -  =  =  =  =   (correct).


ANSWER.  There are two answers: the running speed can be 4 miles per hour and/or 6 miles per hour.

Solved.

RELATED QUESTIONS
i need your help to this problem. can you help me?here's the prob. A man is at a point (answered by mananth)

Len is planning a three hour trip down a river and back to his starting point. He knows... (answered by josmiceli)

Rob is planning a three hour trip down the Allenem River and back to his starting point. (answered by mananth)

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)

A man who can row in still water at 5 mph heads directly across a river flowing at 6 mph. (answered by stanbon)

Kyle is planning a 3 hour trip down a river and back to his starting point. He knows he... (answered by macston)

A man takes 5 hours and 20 minutes to row 6 miles up a river and back. If he can row 3... (answered by ikleyn)

Liam is planning a three hour trip down the East River and back to his starting point. He (answered by mananth,richwmiller)

A man can row downstream 18 km at the same time that he can row 10 km upstream. What is... (answered by scott8148)