Answer:
1 hour 26 Minutes
Step-by-step explanation:
Tanya needs 2 hours to do the job.
Pat needs 5 hours to do this same job.
Tanya's rate [tex]=\frac{1}{2}[/tex]
Pat's rate[tex]=\frac{1}{5}[/tex]
Let the number of hours it will take both of them =x
Rate when two of them work together [tex]=\frac{1}{x}[/tex]
Therefore:
[tex]\frac{1}{2}+\frac{1}{5}=\frac{1}{x}\\$Taking lowest common multiple$\\\frac{5+2}{10}=\frac{1}{x}\\\\\frac{7}{10}=\frac{1}{x}\\\\$Cross multiply$\\7x=10\\x=1.43$ hours[/tex]
[tex]0.43 X 60 =25.8 \approx 26$ minutes[/tex]
Therefore: 1.43 hour = 1 hour 26 Minutes
It will take both of them approximately 1 hour 26 minutes to the job.
