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4 years ago

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A crew will arrive in one week and begin filming a city for a movie. The mayor is desperate to clean the city streets before fil

ming begins. Two teams are available, one that requires 200 hours and one that requires "400" hours. If the teams work together, how long will it take to clean all of the streets? Is this enough time before the cameras begin rolling?

1 answer:

Zigmanuir [339]4 years ago

6 0

Answer:

See below in bold.

Step-by-step explanation:

You work in fractions of the city streets done per hour:

1/200 + 1/400 = 1 /x where x is the number of hours taken by 2 teams.

Multiply through by the LCM 400x:

2x + x = 400

3x = 400

x = 133.33 hours.

As there are 168 hours in a week they will have enough time.

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$\boxed{\sf x=-2}$

$\boxed{\sf y=-4}$

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<u>First, Let's solve for x in -2x+2y=-4:</u>

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<u>Subtract 2y from both sides:</u>

$\sf -2x+2y-2y=-4-2y$

$\sf -2x=-4-2y$

<u>Divide both sides by -2:</u>

$\sf \cfrac{-2x}{-2}=-\cfrac{4}{-2}-\cfrac{2y}{-2}$

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<u>Now, we'll substitute x=y+2 to 3x+3y=-18:</u>

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$\sf 6+6y=-18$

<u>Now, let's solve for y in 6+6y=-18</u>

$\sf 6+6y=-18$

<u>Subtract 6 from both sides:</u>

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$\sf 6y=-24$

<u>Divide both sides by 6:</u>

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<u>_____________________________________</u>

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Step-by-step explanation:

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