Question

Tamara and Jason work at a widget factory. Tamara arrived at work before Jason and began making widgets. Tamara had already made 20 widgets when Jason began his work. Tamara was producing widgets at a rate of 8 widgets per hour. Jason was able to produce widgets at a rate of 12 widgets per hour. At some point, Tamara and Jason will have produced the same number of widgets.

Answer 1

Answer:

See explanation!

Step-by-step explanation:

The remaining question reads:

Part A: Write a system of equations to represent the situation. Let x = hours and y = widgets.

Part B: How much time does it take for Tamara and Jason to produce the same number of widgets?

Part C: How many widgets will Tamara and Jason have produced?

-------------------------------------------------------------------------------------------------------------

To solve this problem we can construct an linear algebraic expression for each person, principally denoted as:

$y=ax+c$

where

$y$ :is our dependent variable (which is a function of $x$)

$x$ :is our independent variable

$a$ :is the slope

$c$ :is the y-intercept constant value (if any present)

Part A: Write a system of equations to represent the situation. Let x = hours and y = widgets.

Tamara

Has already made 20 widgets and produces at a rate of 8 widgets per hour thus here $c=20$ and $a=8$, so Tamara's equation reads:

$y_{T}=8x+20$

Jason

Has not produced any widgets yet and produces at a rate of 12 widgets per hour thus here $c=0$ and $a=12$, so Jason's equation reads:

$y_{J}=12x$

So the system of equations will be

$y_{T}=8x+20\\y_{J}=12x$

Part B: How much time does it take for Tamara and Jason to produce the same number of widgets?

Since we want to find the amount of time (i.e. the value of $x$ ) it takes for both of them to produce the same number of widgets we can just equate the two equations ans solve for $x$ as follow:

$y_{T}=y_{J}\\8x+20=12x\\8x-12x=-20\\-4x=-20\\x=\frac{-20}{-4}\\ x=5$

So it takes them 5 hours to produce the same amount of widgets.

Part C: How many widgets will Tamara and Jason have produced?

Now we can simply plug in the value of $x=5$ in any of the two equations (i.e. either for Tamara or Jason) to find the number of widgets produced.

$y_{T}=8(5)+20=40+20=60$

So in a time-space of 5 hours Each will have produced 60 widgets and in total will be 60+60 = 120 widgets.