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

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)   (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 21

CREATE SYSTEM OF EQUATIONS USING TRAVEL RATE RULE

SOLVE THE SYSTEM FOR THE UNKNOWN VARIABLES
-

-

-

----------and this is what the question asked for.
.
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the speed of her boat in still water
Let = the speed of the current
= her speed going downstream
= her speed going upstream
---------------------------------------------
Equation for going downstream:
(1)
Equation for going upstream:
(2)
---------------------------
Add the equations:
(1)
(2)
-------------------

--------------
the speed of her boat in still water is 6.5 mi/hr
--------------
check answer:
(1)
(1)
(1) mi/hr
and
(2)
(2)
(2)
OK

Answer by MathTherapy(10555)   (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 + C = 7 ------- eq (i)
____S - C = 6 ------- eq (ii)
Add eqs (ii) & (i) to get value of S. You should get:
That's it...nothing COMPLEX!!
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