SOLUTION: A boat traveled downstream a distance of 50 mi and then came right back. If the speed of the current was 20 mph and the total trip took 3 hours and 20 minutes, find the average spe

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Question 1066350: A boat traveled downstream a distance of 50 mi and then came right back. If the speed of the current was 20 mph and the total trip took 3 hours and 20 minutes, find the average speed of the boat relative to the water.
Found 4 solutions by josgarithmetic, Boreal, josmiceli, MathTherapy:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
               SPEED        TIME           DISTANCE

DOWN           r+20                      50

UP             r-20                      50

TOTAL


Solve this for r.
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
speed of boat is x
speed of current is 20 mph
x+20* t1=50, so t1=50/(x+20)
x-20*t2=50, so t2=50/(x-20)
50/(x+20)+50/(x-20)=10/3, where 10/3 is hours.
multiply everything by (x+20)(x-20 or x^2-400
50(x-20)+50(x+20)=(10/3)x^2-4000/3; the left side is equal to 100x
(10/3)x^2-100x-4000/3=0
multiply everything by 3 then divide everything by 10.
10x^2-300x-4000=0
x^2-30x-400=0
(x-40)(x+10)=0
x=40 mph, only positive root ANSWER.
goes 60 mph downstream and takes 5/6 hr or 50 minutes
goes 20 mph upstream and takes 2.5 hours or 150 minutes.
That takes 200 minutes, which is 3h20m
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the speed of the boat with no current in mi/hr
= the speed of the boat going downstream in mi/hr
= the speed of the boat going upstream in miles/hr
Let = time in hrs to go downstream
= time in hrs to go upstream
-----------------------------------------
Going downstream:
(1)
Going upstream:
(2)
-----------------------------------
(2)
(2)
and
(1)
Plug (1) into (2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)









( can't use the negative solution )
--------------------
The speed of the boat with no current is 40 mi/hr
--------------------
check:
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
(2)
(2)
(2)
OK




Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!

A boat traveled downstream a distance of 50 mi and then came right back. If the speed of the current was 20 mph and the total trip took 3 hours and 20 minutes, find the average speed of the boat relative to the water.
Let speed in still water be S

Then average speed downstream = S + 20

Average speed upstream: S – 20

We then get the following TIME equation: 



50(3)(S – 20) + 50(3)(S + 20) = 10(S + 20)(S – 20) ------- Multiplying by LCD, 3(S  + 20)(S – 20)











(S - 40)(S + 10) = 0

S, or speed of boat in still water =    	OR   	  S = - 10 (ignore) 

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