SOLUTION: Carol requires 3 hours to go downstream 21 miles in her motorized boat. Her return trip upstream requires 3 1/2 hours. Assuming that Carol's boat motor runs at a constant pace, fin

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Carol requires 3 hours to go downstream 21 miles in her motorized boat. Her return trip upstream requires 3 1/2 hours. Assuming that Carol's boat motor runs at a constant pace, fin      Log On


   

Question 1057326: Carol requires 3 hours to go downstream 21 miles in her motorized boat. Her return trip upstream requires 3 1/2 hours. Assuming that Carol's boat motor runs at a constant pace, find the speed of her boat in still water.
Found 3 solutions by josgarithmetic, josmiceli, MathTherapy:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
No; her motorboat does not run at a constant pace.
If you will describe this exercise correctly, I will solve most of it for you.

I see how this SHOULD be written:
Carol requires 3 hours to go downstream 21 miles in her motorboat. Her return trip upstream requires 3 1/2 hours. Find the speed of her motorboat in still water.

The "assuming" part is wrong.


Let c be the speed of the river current.

SETUP TABLE OF DATA 
                       speed        time        distance

DOWN                   r+c          3            21

UP                     r-c         3%261%2F2        21


CREATE SYSTEM OF EQUATIONS USING TRAVEL RATE RULE
system%28%28r%2Bc%29%2A3=21%2C%28r-c%29%283%261%2F2%29=21%29



SOLVE THE SYSTEM FOR THE UNKNOWN VARIABLES
-
system%28r%2Bc=7%2Cr-c=21%2F%287%2F2%29%29
-
system%28r%2Bc=7%2Cr-c=3%2F2%29
-
r%2Bc%2Br-c=7%2B3%2F2
2r=%2814%2B3%29%2F2
highlight%28r=17%2F4%29----------and this is what the question asked for.
%284%261%2F4%29%28miles%2Fhour%29.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of her boat in still water
Let +c+ = the speed of the current
+s+%2B+c+ = her speed going downstream
+s+-+c+ = her speed going upstream
---------------------------------------------
Equation for going downstream:
(1) +21+=+%28+s+%2B+c+%29%2A3+
Equation for going upstream:
(2) +21+=+%28+s+-+c+%29%2A3.5+
---------------------------
Add the equations:
(1) +s+%2B+c+=+7+
(2) +s+-+c+=+6+
-------------------
+2s+=+13+
+s+=+6.5+
--------------
the speed of her boat in still water is 6.5 mi/hr
--------------
check answer:
(1) +s+%2B+c+=+7+
(1) +6.5+%2B+c+=+7+
(1) +c+=+.5+ mi/hr
and
(2) +s+-+c+=+6+
(2) +6.5+-+c+=+6+
(2) +c+=+.5+
OK

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Carol requires 3 hours to go downstream 21 miles in her motorized boat. Her return trip upstream requires 3 1/2 hours. Assuming that Carol's boat motor runs at a constant pace, find the speed of her boat in still water.
With speed in still water being S, we get the following system of TOTAL AVERAGE-SPEED equations: 

S+%2B+C+=+21%2F3_______S + C = 7 ------- eq (i)

S+-+C+=+21%2F%283%261%2F2%29____S - C = 6 ------- eq (ii)

Add eqs (ii) & (i) to get value of S. You should get: highlight_green%28matrix%281%2C4%2C+S%2C+%22=%22%2C+6.5%2C+mph%29%29

That's it...nothing COMPLEX!!