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 g

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?

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Eden 2 weeks 2022-01-01T17:24:06+00:00 1 Answer 0 views 0

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    2022-01-01T17:25:31+00:00

    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.

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