Checkpoint: Applications of Rational Equations Solution

Solve.

Lindsey and Haven are painting a fence in their backyard. Alone, Lindsey can paint the fence in 9 hours. Together they are able to paint the fence in 5 hours. How long would it take Haven to paint the fence alone?

	Lindsey		Haven		Together
time:	9		t		5
rate:	$\frac{1}{9}$	+	$\frac{1}{t}$	=	$\frac{1}{5}$

$\frac{1}{9} + \frac{1}{t} = \frac{1}{5} \begin{matrix} LCD (9, t, 5) = 45 t \end{matrix} 45 t (\frac{1}{9} + \frac{1}{t} = \frac{1}{5}) or \frac{1}{9} (\frac{5 t}{5 t}) + \frac{1}{t} (\frac{45}{45}) = \frac{1}{5} (\frac{9 t}{9 t}) 5 t + 45 = 9 t 45 = 4 t t = \frac{45}{4} t = 11 \frac{1}{4}$

Note

Q: If the total time is known, where will the variable be in the equation?  

A: In the place for Haven’s rate and time.

It would take Haven $11 \frac{1}{4}$ hours to paint the fence alone.