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MakcuM [25]
3 years ago
12

Working together, Candice and Ximena painted a fence in 8 hours. Last year, Ximena painted the fence by herself. The year before

, Candice painted it by herself, but took 12 hours less than Ximena took. How long did Candice and Ximena take, when each was painting alone?
Mathematics
1 answer:
makkiz [27]3 years ago
3 0

Answer: Time taken by Ximena to paint the fence alone  = 24 hours

Time taken by Candice to paint the fence alone = 12 hours

Step-by-step explanation:

Let x= Time taken by Ximena to paint the fence alone .

Time taken by Candice to paint the fence alone = x-12

As per given , we have

\dfrac{1}{x}+\dfrac{1}{x-12}=\dfrac{1}{8}\\\\\Rightarrow\ \dfrac{x-12+x}{x(x-12)}=\dfrac{1}{8}\\\\\Rightarrow\ 8(2x-12)=x^2-12x\\\\\Rightarrow\ 16x-96=x^2-12x\\\\\Rightarrow\ x^2-12x-16x+96=0\\\\\Rightarrow\ x^2-28x+96=0\\\\\Rightarrow\ x^2-4x-24x+96=0\\\\\Rightarrow\ x(x-4)-24(x-4)=0\\\\\Rightarrow\ (x-4)(x-24)=0\\\\\Rightarrow x=4, 24

if x= 4

Time taken by Ximena = 4 hours

Time taken by Candice = 4-12 hours =-8 hours which is not possible. (time cannot be negative)

Therefore, x= 24

Such that

Time taken by Ximena to paint the fence alone  = 24 hours

Time taken by Candice to paint the fence alone = 24-12=12 hours

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Step-by-step explanation:

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The total withdrawn amount by 27 people = 100 × 27

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Using Unit Rates to compare Ratios continued
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Brandon

Step-by-step explanation:

GIVEN: Branden and Pete each play running back. Branden carries the ball 75 times for  550 yards, and Pete has 42 carries for 380 yards.

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Total yards traveled by Brandon =550\text{yards}

No. of times ball carried by Brandon =75\text{ times}

Average yards per carry for Brandon =\frac{\text{total yards traveled}}{\text{number of times ball carried}}

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Total yards traveled by Pete =380\text{ yards}

No. of times ball carried by Pete =42\text{ times}

Average yards per carry for Pete =\frac{\text{total yards traveled}}{\text{number of times ball carried}}

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As the number of yards per carry is higher for Brandon , therefore he runs farther per carry.

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3 years ago
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