SOLUTION: Ina Crespo rowed 18 miles down the Habashabee River in 2 hours, but the return trip took her 4.5 hours. Find the rate Ina rows in still river and the rate of the current. Let x rep

Algebra ->  Linear-equations -> SOLUTION: Ina Crespo rowed 18 miles down the Habashabee River in 2 hours, but the return trip took her 4.5 hours. Find the rate Ina rows in still river and the rate of the current. Let x rep      Log On


   

Question 1102599: Ina Crespo rowed 18 miles down the Habashabee River in 2 hours, but the return trip took her 4.5 hours. Find the rate Ina rows in still river and the rate of the current. Let x represent the rate Ina can row in still river and let y represent the rate of the current.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
b=2, time downstream
u=4.5, time upstream
d=18, distance each way
r, unknown speed no current
c, unknown speed of current 
                SPEED       TIME       DISTANCE
DOWNSTREAM      r+c          b          d
UPSTREAM        r-c          u          d

system%28r%2Bc=d%2Fb%2Cr-c=d%2Fu%29

-
2r=d%2Fb%2Bd%2Fu
2r=%28ud%2Bbd%29%2F%28bu%29
highlight_green%28r=%28ud%2Bbd%29%2F%282bu%29%29
-
2c=d%2Fb-d%2Fu
2c=%28ud-bd%29%2F%28bu%29
highlight_green%28c=%28ud-bd%29%2F%282bu%29%29


-
substitutegivenvalues:
r=%282%2A18%2B4.5%2A18%29%2F%282%2A2%2A4.5%29
highlight%28r=6.5%29

c=%284.5%2A18-2%2A18%29%2F%282%2A2%2A4.5%29
highlight%28c=2.5%29

Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
Ina Crespo rowed 18 miles highlight%28cross%28down%29%29 downstream the Habashabee River in 2 hours, but the return trip took her 4.5 hours.
Find the rate Ina rows in still highlight%28cross%28river%29%29 water and the rate of the current.
Let x represent the rate Ina can row in still highlight%28cross%28river%29%29 water and let y represent the rate of the current.
~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let x represent the rate Ina can row in still water (in miles per hour, mph).

Let y represent the rate of the current.


The effective speed going downstream is 

Distance%2FTime = 18%2F2 = 9 mph.


The effective speed going downstream is the SUM of the Ina' speed in still water and the rate of the current. 
It gives you your first equation

x + y = 9.    (1)



The effective speed going upstream is 

Distance%2FTime = 18%2F4.5 = 4 mph.


The effective speed going upstream is the DIFFERENCE of the Ina' speed in still water and the rate of the current. It gives you your second equation

x - y = 4.    (2)


Thus you have this system of two equations in 2 unknowns

x + y = 9,    (1)   and
x - y = 4.    (2)


Add the two equations. You will get

2x = 9 + 4 = 13  ====>  u = 13%2F2 = 6.5 mph.


So, you just found the Ina' speed in still water.  It is  6.5 miles per hour.

Then from the equation (1) you get  y = 9 - 6.5 = 2.5 mph is the current rate.


Answer.  The Ina' speed in still water is  6.5 mph.

         The current rate is 2.5 mph.

Solved.


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It is a typical and standard Upstream and Downstream round trip word problem.
You can find many similar fully solved problems on upstream and downstream round trips with detailed solutions in lessons
    - Wind and Current problems
    - More problems on upstream and downstream round trips
    - Wind and Current problems solvable by quadratic equations
    - Unpowered raft floating downstream along a river
    - Selected problems from the archive on the boat floating Upstream and Downstream
in this site.

Read them attentively and learn how to solve this type of problems once and for all.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the section "Word problems",  the topic "Travel and Distance problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.