SOLUTION: I would be so happy if someone can help me work this out please. Ina Crespo rowed 12 miles down the Habashabee River in 1.5 ​hours, but the return trip took her 4 hours. Fin

Algebra ->  Systems-of-equations -> SOLUTION: I would be so happy if someone can help me work this out please. Ina Crespo rowed 12 miles down the Habashabee River in 1.5 ​hours, but the return trip took her 4 hours. Fin      Log On


   



Question 1125421: I would be so happy if someone can help me work this out please.
Ina Crespo rowed 12 miles down the Habashabee River in 1.5 ​hours, but the return trip took her 4 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.
d=r•t
Downstream x+y
Upstream x−y
Ina can row ____mph in still water.

Answer by ikleyn(52873) About Me  (Show Source):
You can put this solution on YOUR website!
Let x represent the rate Ina can row in still water and 
let y represent the rate of the current. 


Then  her  effective speed downstream  is  x+y   miles per hour,
while her  effective speed upstream    is  x-y  miles per hour.


    // It is first major point you need understand and use in this sort of problems.


Now, "speed" equation for boat floating downstream is 

12%2F1.5 = u + v    (1)    (speed downstream = the distance divided by time downstream)


Next, "speed" equation for boat floating upstream is 

12%2F4 = u - v    (2)    (speed upstream = the distance divided by time  duptream)


    // It is the second major point in solving such problems: you must understand and write these equation automatically !


Simplify equations (1) and (2)


u + v =  8     (3)
u - v =  3     (4)


Now add equations (3) and (4) to eliminate "v". You will get


2u = 8 + 3 = 13  ====>  u = 13%2F2 = 6.5.


Thus you just found the boat' speed in still water. It is 6.5 miles per hour.


Next, you can find the current rate from eq(4)  v = 8 - u = 8 - 6.5 = 1.5 miles per hour.


Answer.  The boat' speed in still water is 6.5 miles per hour.

         The current speed is 1.5 miles per hour.



Solved.  I advise you to make the check on your own.


         After making the check, you will understand the problem and the solution MUCH better.

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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, where you will find other similar solved problems with detailed explanations.

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.