SOLUTION: A boat traveled downstream a distance of 36 mi and then came right back. If the speed of the current was 12 mph and the total trip took 4 hour find the average speed of the boat re

Algebra ->  Human-and-algebraic-language -> SOLUTION: A boat traveled downstream a distance of 36 mi and then came right back. If the speed of the current was 12 mph and the total trip took 4 hour find the average speed of the boat re      Log On


   

Question 1141775: A boat traveled downstream a distance of 36 mi and then came right back. If the speed of the current was 12 mph and the total trip took 4 hour find the average speed of the boat relative to the water.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52787) About Me  (Show Source):
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
r, unknown speed of boat without current
C=12, speed of current
T=4, total trip time
D=36, distance traveled in each direction 
                SPEED        TIMES            DISTANCE

DOWNSTREAM        r+C         D/(r+C)             D

UPSTREAM         r-C          D/(r-C)            D

TOTALS                       T

D%2F%28r%2BC%29%2BD%2F%28r-C%29=T
Solve for r, and then substitute the given values.

Algebra steps may lead to: r%5E2-%282D%2FT%29r-C%5E2=0

If substitute the given values here, then r%5E2-18r-144=0.
You may find this factorable as %28r-24%29%28r%2B6%29=0.
highlight%28r=24%29