Given the rates:
[tex]\begin{gathered} \frac{1}{t}=Sarah^{\prime}s\text{ }Rate \\ \\ \frac{1}{t+3}=Heidi^{\prime}s\text{ }Rate \\ \\ \frac{1}{2}=Rate\text{ }working\text{ }together \end{gathered}[/tex]
Add their rates of cleaning to get rate working together:
[tex]\frac{1}{t}+\frac{1}{t+3}=\frac{1}{2}[/tex]
Solving for t:
[tex]\begin{gathered} \frac{2(t+3)+2t-t(t+3)}{2t(t+3)}=0 \\ \\ \frac{2t+6+2t-t^2-3t}{2t(t+3)}=0 \\ \\ \frac{t+6-t^2}{2t(t+3)}=0 \\ \\ -t^2+t+6=0 \\ \\ (t+2)(t-3)=0 \end{gathered}[/tex]
Hence:
t = -2
t = 3
Time can't be negative; then:
Heidi's time: t + 3
3 + 3 = 9
ANSWER
It will take Heidi 9 hrs to clean garage working alone
