SOLUTION: Ina Crespo rowed 20 miles down the Hashabee River in 2 hours, but the return trip took her 5 hours. Find the rate Ina rows in still water and the rate of the current. Let x represe

Question 800877: Ina Crespo rowed 20 miles down the Hashabee River in 2 hours, but the return trip took her 5 hours. Find the rate Ina rows in still water and the rate of the current. Let x represent the rate Ina can row in still water and let y represent the rate of the current water.
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39628) (Show Source): You can put this solution on YOUR website!
x = rate in still water
y = rate of the current water
(Really, speeds, not rates, but certainly yes, ratios)

WHICHWAY_____________speed_______________time____________distance
DOWN_________________x+y_________________2_______________(___)
UP___________________x-y_________________5_______________(___)

Be aware, we use r*t=d, for uniform rates for movement or travel or transport, r for rate, t for time, d for distance.
Also that the speeds are in order, .

Completing the data table,

WHICHWAY_____________speed_______________time____________distance
DOWN_________________x+y_________________2_______________(x+y)2
UP___________________x-y_________________5_______________(x-y)5
Total_____________________________________________________20

That is the extent of the data analysis. This information gives you a distance sum of ,

Which is a an infinite set of solutions for x and y, but with some restrictions.
You can easily enough find those restrictions symbolically, and you could also make the linear graph and see the restrictions on x and y graphically.

Any solution, (x,y) must be in the Quadrant 1:

miles per hour and miles per hour;
You would pick one variable and assign a value and compute the corresponding value of the other variable.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
boat speed =x mph
current speed =y mph
against current 5 hours
with current 2 hours

Distance against 20 miles distance with 20 miles
t=d/r against current -
20.00 / ( x - y )= 5.00
5.00 ( x - y ) = 2.00
5.00 x - 5.00 y = 20.00 ....................1

20.00 / ( x + y )= 2.00
2.00 ( x + y ) = 20.00
2.00 x + 2.00 y = 20.00 ...............2
Multiply (1) by 2.00
Multiply (2) by 5.00
we get
10.00 x + -10.00 y = 40.00
10.00 x + 10.00 y = 100.00
20.00 x = 140.00
/ 20.00
x = 7.00 mph

plug value of x in (1) y
5.00 x -5.00 y = 20.00
35.00 -5.00 -35.00 = 20.00
-5.00 y = 20.00
-5.00 y = -15.00 mph
y = 3.00
boat speed 7.00 mph
current speed 3.00 mph

m.ananth@hotmail.ca

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