+0  
 
+1
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10
avatar+475 

A boat can cover 12 km up the stream and 75% of that distance down the stream in 6 hours. Find the speed of the boat in still water if the speed of the stream is 41 2/3 meters per minute.

 Nov 18, 2020
 #1
avatar+2246 
+2

Not entirely sure about this one... Try setting an equation. Let x be the speed of the boat.

 

(x+41 2/3) + 3/4(41 2/3-x)= 3/4(12) + 12 = 21

 Nov 18, 2020
 #2
avatar+114098 
+1

Convert  speed in m/min to km /h

41 +2/3 m / min x 60 min  = 2500 m/ hr =  2.5 km / hr

 

Let R be the  rate of the boat in still water

 

[75% of 12  = 9]

 

And note  that   D /R  = Total time

 

Rate downstream  = R + 2.5        Rate upstream = R - 2.5

 

Distance downstream / Rate Downstream   +  Distance upstream/ Rate upstream  = Total time

 

12 / [ R + 2.5]   +  9 / [ R - 2.5 ]  =  6

 

(12 [ R-2.5] + 9 [ R + 2.5] )  / [  (R+ 2.5 ) (R -2.5)] = 6

 

[ 12 R  - 30  + 9R + 22.5]/ (R^2 - 6.25)  = 6

 

21R - 7.5  =  6 [ R^2 - 6.25 ]

 

21R - 7.5  = 6R^2 - 37.5       rearrange as

 

6R^2 - 21R  - 30  =  0        divide through by 3

 

2R^2  - 7R - 10  =  0 

 

Using the quadratic formula

 

R = (  7 +  sqrt [ ( 7^2 - (4)*(2) *( -10)] ) / ( 2 * 2)  =   ( 7 + sqrt ( 129)) / 4  ≈  4.6 km/h

 

 

cool cool cool

 Nov 18, 2020
edited by CPhill  Nov 18, 2020
 #3
avatar+2246 
+2

Darn, I think I made a mistake! Nice job, CPhill and for the op check his answer instead :)

CalTheGreat  Nov 18, 2020
 #9
avatar
0

CPhill: This line:  12 / [ R + 2.5]   +  9 / [ R - 2.5 ]  =  6 should read: 12/[R-2.5] + 9/[R+2.5] = 6  and that gives R =5 km/h.

Guest Nov 18, 2020
 #4
avatar+475 
+1

but cphill it would be + or -??

 Nov 18, 2020
 #5
avatar+114098 
0

Has to be a plus

 

7 - sqrt (129)  is a negative

 

And the rate of the  boat in still water  is always positive

 

cool cool cool

CPhill  Nov 18, 2020
 #6
avatar+475 
+1

Right, thankss!!!

HelpBot  Nov 18, 2020
 #7
avatar
0

 Rate * time = distance     41 2/3 meters/min = 2.5 km/hr

time = distance/r

6= 12/(r-2.5)  + 9 /(r+2.5)

6 (r-2.5)(r+2.5) =12 (r + 2.5) + 9 ( r-2.5)

6 (r^2 -6.25) =

6 r^2 -37.5      = 12 r + 30 + 9r - 22.5

6r^2 -21r - 45 =0

r= 5 km/hr    (via quadratic equation)

 

CHECK:   12 km / (5-2.5)km/hr    +   9 km / (5+2.5)km/hr  =    6 hours     CHECK !

 Nov 18, 2020
 #8
avatar
0

12 / [ R + 2.5]   +  9 / [ R - 2.5 ]  =  6      Where cphill went wrong....this should be:

 

12 / [ R - 2.5]   +  9 / [ R + 2.5 ]  =  6

 Nov 18, 2020
 #10
avatar+475 
+1

i get it! i probably did the factoring wrong as well! Thank you very much!!!!! :D

 Nov 19, 2020

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