Question

Working alone, Jess can rake leaves off a lawn in 50 minutes. Working alone, cousin Tate can do the same job in 30 minutes. Today they are going to work together, Jess starting t one end of the lawn and Tate starting simultaneously at the other end. In how many minutes will they meet and thus have the lawn completely raked?

Answer 1

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 $\frac{1}{50}$.

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 $\frac{1}{30}$.

Part of work done by both in one minute would be $\frac{1}{t}$.

We can represent our given information in an equation as:

$\frac{1}{50}+\frac{1}{30}=\frac{1}{t}$

Let us solve for t.

$\frac{1}{50}*150t+\frac{1}{30}*150t=\frac{1}{t}*150t$

$3t+5t=150\\\\8t=150$

$\frac{8t}{8}=\frac{150}{8}\\\\t=18.75$

Therefore, the lawn will be completely raked in 18.75 minutes and they will meet after 18.75 minutes.