Given that:
- Sylvia can pick a pint of raspberries in 20 minutes working alone.
- Jasmine and Sylvia can complete the job in 8 minutes if they work together.
You can use the following Rate for Work Formula in order to solve the exercise:
[tex]\frac{t}{a}+\frac{t}{b}=1[/tex]Where "t" is the time for objects A and B to complete the work together, "a" is the time needed for object A to complete the work alone, and "b" is the time for object B to complete the work alone.
In this case, you can identify that:
[tex]\begin{gathered} t=8\text{ } \\ a=20\text{ } \end{gathered}[/tex]Therefore, by substituting values into the formula and solving for "b", you can determine how long it would take (in minutes) for Jasmin to pick a pint of raspberries working alone:
[tex]\frac{8}{20}+\frac{8}{b}=1[/tex][tex]\frac{8}{b}=1-\frac{8}{20}[/tex][tex]\frac{8}{b}=1-\frac{8}{20}[/tex][tex]8=(\frac{3}{5})(b)[/tex][tex](8)(\frac{5}{3})=b[/tex][tex]b\approx13.3[/tex]Hence, the answer is:
[tex]13.3\text{ }minutes\text{ \lparen Approximately\rparen}[/tex]