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 Rational Word Problem

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Karen and Benjamin are ecologists studying forest regeneration. Working together, they can count the seedlings on a research site in 2h. It takes Karen 8h to count on her own. How long would it take Benjamin to count the seedlings on his own? Give the answer to one decimal place necessary. Show your work

 Jul 23, 2021

2+0 Answers

 #1
avatar+129850 
+1

Let Benjamin's  rate per hour   = 1/x

 

(1/8  + 1/x)   =     ( x + 8)  /  (8x)

 

Invert  the  right side  and set it  =   2

 

So

 

8x / ( 8 + x)  =   2

 

8x  = 2 ( 8 + x)

 

8x  = 16 + 2x

 

8x  - 2x  = 16

 

6x  = 16

 

x   =  16/6   =  8/3 hrs.   ≈  2.7  hours  working on his own

 

 

cool cool cool

 Jul 23, 2021
 #2
avatar+37159 
0

1/8  + 1/b  = 1/2

1/b = 3/8

b = 8/3 hr

 Jul 23, 2021

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