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Math Question Algebra 2?
Bill rowed 30km upstream against a 2km/h current and back again in a total of 8h. How fast can he row in still water?
2 Answers
- ranjankarLv 79 years agoFavorite Answer
LET HIS SPEED OF ROWING IN STILL WATERS BE X KM/ HOUR
UPSTREAM
--------------------
SPEED = ( X- 2) KM/ HOUR
DOWNSTREAM
---------------------------
SPEED = ( X+2) KM/ HOUR
TIME = DISTANCE / SPEED
30 / (X+2) + 30 / ( X-2) = 8 HOURS
MULTIPLY BOTH SIDES BY (X+2) ( X-2)
30 ( X-2) + 30( X+2) = 8 ( X+2) ( X-2)
30X -60 +30X +60 = 8X^2 -32
8X^2 -60X - 32 = 0
2X^2 -15X -8 = 0
2X^2 +X -16X -8 = 0
X ( 2X+1) -8( 2X +1) = 0
( X-8) ( 2X+1) = 0
REJECTING THE NEGATIVE VALUE , X = 8 KM/ HOUR ANSWER
CHECK
30 / (8-2) = 5 HOURS
30/ ( 8+2) = 3 HOURS
5+3 = 8 HOURS
- 9 years ago
TYPE......................RATE............TIME................DISTANCE
************************************************************************
Upstream...............R - 2............................................30
Downstream..........R + 2...........................................30
Time = Dist / Rate
TYPE......................RATE............TIME................DISTANCE
************************************************************************
Upstream...............R - 2...............30/(R - 2)................30
Downstream..........R + 2..............30/(R + 2)...............30
Time UP + Time DOWN = 8
30...........30
-------..+ -------- = 8.....................Multiply each term by (R-2)(R+2) = R²-4
R - 2.....R + 2
30(R + 2) + 30(R - 2) = 8(R² - 4)
30R + 60 + 30R - 60 = 8R² - 32
60R = 8R² - 32............................Divide all terms by 4
15R = 2R² - 8
0 = 2R² - 15R - 8
0 = (2R + 1)(R - 8)
R = - 1/2 NO .....OR R = 8
ANSWER................8 mph rows Bill in still water
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