Answer:
18.75 minutes.
Step-by-step explanation:
Let t represent minutes taken to complete the job by Jess and Tate working together.
We have been given that working alone, Jess can rake leaves off a lawn in 50 minutes, so part of work done by Jess in 1 minute would be [tex]\frac{1}{50}[/tex].
We are also told that working alone, cousin Tate can do the same job in 30 minutes, so part of work done by Tate in 1 minute would be [tex]\frac{1}{30}[/tex].
Part of work done by both in one minute would be [tex]\frac{1}{t}[/tex].
We can represent our given information in an equation as:
[tex]\frac{1}{50}+\frac{1}{30}=\frac{1}{t}[/tex]
Let us solve for t.
[tex]\frac{1}{50}*150t+\frac{1}{30}*150t=\frac{1}{t}*150t[/tex]
[tex]3t+5t=150\\\\8t=150[/tex]
[tex]\frac{8t}{8}=\frac{150}{8}\\\\t=18.75[/tex]
Therefore, the lawn will be completely raked in 18.75 minutes and they will meet after 18.75 minutes.
