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Wize High School Grade 12 Pre-Calculus Textbook > Rational Functions

Applications of Rational Functions

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Example: Applications of Rational Functions

Abigail can run 3 km/hr3 \text{ km/hr} faster than her younger brother Griffin can walk. If Abigail ran 12 km12 \text{ km} in the same time it took Griffin to walk 8 km8 \text{ km}, what is the speed of each Abigail and Griffin?

Let xx be Griffin's speed.

Speed (Rate)TimeDistanceAbigailx+312x+312Griffinx8x8\begin{array}{|c|c|c|c|}\hline &\textbf{Speed (Rate)}&\textbf{Time}&\textbf{Distance}\\\hline\\ \text{Abigail}&x+3&\displaystyle\frac{12}{x+3}&12\\\\\hline\\ \text{Griffin}&x&\displaystyle\frac{8}{x}&8\\\\\hline \end{array} Speed×Time=DistanceSpeed=DistanceTimeTime=DistanceSpeed\begin{array}{rcl} \text{Speed}\times\text{Time}&=&\text{Distance}\\\\ \text{Speed}&=&\displaystyle\frac{\text{Distance}}{\text{Time}}\\\\ \text{Time}&=&\displaystyle\frac{\text{Distance}}{\text{Speed}} \end{array}

We know that Abigail ran 12km in the same time that Griffin walked 8km. Therefore,

12x+3=8x12x=8(x+3)12x=8x+244x=24x=6\begin{array}{rcl} \displaystyle\frac{12}{x+3}&=&\displaystyle\frac{8}{x}\\\\ 12x&=&8(x+3)\\\\ 12x&=&8x+24\\\\ 4x&=&24\\\\ x&=&6 \end{array}

So, Griffin walked 6km/hr6km/hr and Abigail ran 9km/hr9km/hr.

Practice: Applications of Rational Functions (Work)

Jaycee takes 2 hours to cook 50 eggs. Caycee takes 3 hours to cook 45 eggs. Working together, how long should it take them to cook 150 eggs?

Practice: Applications of Rational Functions

Two hoses are being used to fill Kay & Alice's pool. One hose can fill the pool in 10 hours and the second hose can fill it in 12 hours. The pool's drain can empty the pool in 8 hours. If the two hoses fill the pool together, and the drain is open (by mistake), how long will it take to fill the pool?

Practice: Applications of Rational Functions

8 men and 12 boys can build a shed in 10 hours. 6 men and 8 boys can build a shed in 14 hours.

a) How long would it take 1 man to build a shed?

b) How long would it take 1 boy to build a shed?
Extra Practice
Applications of Rational Functions
Practice: Applications of Rational Functions
12 men and 8 boys can build a playhouse in 16 hours. 8 men and 10 boys can build a playhouse in 20 hours.
a) How long would it take 1 man to build a playhouse?
Applications of Rational Functions
Practice: Applications of Rational Functions
7 women and 11 girls can make a shelf in 4 hours. 11 women and 5 girls can build a shelf in 6 hours.
a) How long would it take 1 woman to build a shelf?
Applications of Rational Functions
Practice: Applications of Rational Functions
Two hoses are being used to fill Gus's pool. One hose can fill the pool in 8 hours and the second hose can fill it in 5 hours. The pool drain can empty the pool in 6 hours. If the two hoses fill the pool together, and the drain is open (by mistake), how long will it take to fill the pool?
Applications of Rational Functions
Practice: Applications of Rational Functions
Two faucets are being used to fill Sheldon's bathtub. One faucet can fill the tub in 0.25 hours and the second faucet can fill it in 0.125 hours The faucet's drain can empty the tub in 0.15 hours. If the two faucets fill the tub together, and the drain is open (by mistake), how long will it take to fill the tub?
Applications of Rational Functions
Practice: Applications of Rational Functions
Drew takes 4 hours to decorate 250 cookies. Violet takes 5 hours to decorate 340 cookies. Working together, how long should it take them to decorate 600 cookies?
Applications of Rational Functions
Practice: Applications of Rational Functions
Maisy takes 5 hours to paint 16 paintings. Svea takes 7 hours to paint 21 paintings. Working together, how long should it take them to paint 50 paintings?
Applications of Rational Functions
An integer is 4 less than another.
The sum of their reciprocals is 1021\dfrac{10}{21}.
What the the 2 integers?