Question

the temperature in brandon is 57 degrees fahrenheit and it is decreasing by 3 degrees per hour. several miles south in oakley, the temperature is 49 degrees fahrenheit and it is increasing by 5 degrees per hour. in how many hours will the temperature in the two towns be the same?

1. two students are painting strips of wood to make scenery for the school play. henry has painted 14 strips of wood. he can paint 3\\(\frac{1}{2}\\) strips of wood per minute. sandy has painted 10 strips of wood. she can paint 4 strips of wood per minute. after how many minutes will both students have painted the same number of strips of wood?

1. car rental company a charges a $25 fee plus $42.50 per day to rent a car. car rental company b charges a $40 fee plus $37.50 per day to rent a car. for how many days will the cost of a rental car be the same?

1. to ship a package, a shipping company charges $8 for the first pound and $1.20 for each additional pound. a second company charges $5 for the first pound and $1.50 for each additional pound. how many pounds must the package weigh for the shipping cost to be the same for both companies?

1. to travel to the community center after school, simone can take the subway or ride the bus. she can purchase a monthly pass for the subway for an initial fee of $25 and then $0.50 per ride. she can purchase a monthly pass for the bus for an initial fee of $10 and $1.25 per ride. after how many rides will the cost of the subway and the bus be the same?

Explanation:

Problem 12

Step1: Define variables

Let $t$ = minutes elapsed.

Step2: Set up equations for each student

Henry: $14 + 3.5t$
Sandy: $10 + 4t$

Step3: Equate the two expressions

$14 + 3.5t = 10 + 4t$

Step4: Solve for $t$

$14 - 10 = 4t - 3.5t$
$4 = 0.5t$
$t = \frac{4}{0.5} = 8$

Step1: Define variables

Let $d$ = rental days.

Step2: Set up cost equations

Company A: $25 + 42.50d$
Company B: $40 + 37.50d$

Step3: Equate the two costs

$25 + 42.50d = 40 + 37.50d$

Step4: Solve for $d$

$42.50d - 37.50d = 40 - 25$
$5d = 15$
$d = \frac{15}{5} = 3$

Step1: Define variables

Let $w$ = total package weight (pounds).

Step2: Set up cost equations

Company 1: $8 + 1.20(w-1)$
Company 2: $5 + 1.50(w-1)$

Step3: Simplify equations

Company 1: $8 + 1.20w - 1.20 = 6.80 + 1.20w$
Company 2: $5 + 1.50w - 1.50 = 3.50 + 1.50w$

Step4: Equate and solve for $w$

$6.80 + 1.20w = 3.50 + 1.50w$
$6.80 - 3.50 = 1.50w - 1.20w$
$3.30 = 0.30w$
$w = \frac{3.30}{0.30} = 11$

Answer:

8 minutes

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Problem 13