The time it will a take them for both ricardo and his father to finish the painting if they work together is;
t = 2.4 hours
Time for ricardo to paint the set of kitchen cabinets = 6 hours
Time for Ricardo's father to finish painting = 4 hours
This means that ricardo in 1 hour paints 1/6 of the cabinets
His father in 1 hour paints 1/4 of the cabinets
If they work together, in one hour, they would have painted;
1/6 + 1/4 = 5/12 of the cabinet
then 12/12 will be done in; ((12/12) × 1)/(5/12)
⇒ 1 × 12/5
⇒ 2.4 hours
Read more at; https://brainly.com/question/8317268
The correct answer is: " 2 hours and 24 minutes ";
or; write as: " 2.4 hours " .
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Step-by-step explanation:
[tex]\frac{x}{4} + \frac{x}{6} = 1[/tex] ; → { " 1 (one) whole job." }.
We want to solve for "x" ; the total time, in "hours", that will take them if they work together.
What is the LCD (least common denominator of "4" and "6" ?
→ Note that "4 * 6 = 24" ; so, "24" would work, but let's see if we can find the LCD —a number less then "24" ;
4: 2, 4, 12, 16, 20, 24,
6: 1, 2, 3, 6, 12
⇒ We see that "12" is the LCD.
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So, " [tex]\frac{x}{4} = \frac{?}{12}[/tex] " ; to solve for "?" ;
→ 4 * (what value?) = 12 ?
→ 12 ÷ 4 = (that value) ; ⇒ = " 3 " .
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So: [tex]\frac{x}{4} = \frac{(x*3)}{(4*3)} = \frac{3x}{12}[/tex] ;
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Now: " [tex]\frac{x}{6} = \frac{?}{12}[/tex] " ; to solve for "?" ;
→ 6 * (what value?) = 12 ?
→ 12 ÷ 6 = (that value) ; ⇒ = " 2 " .
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So: " [tex]\frac{x}{6} = \frac{(x*2)}{(6*2)} = \frac{2x}{12}[/tex] ;
Now: → [tex]\frac{x}{4} + \frac{x}{6} = 1[/tex] ;
Substitute our converted values:
→ [tex]\frac{3x}{12} + \frac{2x}{12}=1[/tex] ;
Then simplify the "left-hand side" of the equation:
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→ [tex]\frac{3x}{12} + \frac{2x}{12} = \frac{(3x+2x)}{12}[/tex] = [tex]\frac{5x}{12}[/tex] ;
Now, rewrite the simplified equation; and bring down the "1" :
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→ [tex]\frac{5x}{12} = 1[/tex] ;
Now, solve for "x" ; as follows:
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⇒ 5x = ( 1 * 12 ) ;
→ 5x = 12 ;
Now, divide Each Side of the equation by "5" ;
to isolate "x" on one side of the equation; & to solve for "x" (in hours):
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→ 5x / 5 = 12 / 5 ;
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to get: x = (12/5) hours.
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Now: We have (12/5) of 1 hour ; 24/10
Note the exact conversion: " 60 min. = 1 hr." :
So, 12/5 of 60 minutes;
= " [tex]\frac{12}{5}[/tex] * [tex]}\frac{60}{1}[/tex] " (minutes) ;
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The "5" cancels to a "1" ; and the "60" cancels to a "12" :
{since: "60 ÷ 5 = 12" ; & since: "5 ÷ 5 = 1 " .}.
→ And we can rewrite as:
" [tex]\frac{12}{1} * \frac{12}{1}[/tex] " (minutes) = "12 * 12" minutes = 144 minutes.
⇒ " 144 minutes" equals: How many hours? " 144 ÷ 60 = 2.4 hours " ;
or; more specifically:
⇒ We have "2 hours and _(some) minutes".
→ that is; " 2 hours plus 0.4 hour(s) " .
⇒ [tex]\frac{(0.4) hr}{1}*\frac{(60)min}{1 hr} = [(0.4)*(60)] minutes[/tex] ;
= 24 minutes.
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Alternate method:
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(12/5 hours) = (12 ÷ 5) hours = " 2.4 hours " ; (and continue if desired).
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So: The correct answer is: " 2 hours and 24 minutes ";
or; write as: " 2.4 hours " .
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Hope this is helpful to you! Best of luck!
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