Alyssa and Benny were able to dig a garden in 2 hours together. It takes Benny 5 hours to ﬁnish this job alone. Without help, how long would it take Alyssa to ﬁnish this job?

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Alyssa and Benny were able to dig a garden in 2 hours together. It takes Benny 5 hours to ﬁnish this job alone. Without help, how long would it take Alyssa to ﬁnish this job?

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Answer 1 · 2016-04-03T05:46:23

It will take $3$ $3$ hours and $20$ $20$ minutes for Alyssa to finish the job.

Explanation:

Alyssa and Benny can dig a garden in $2$ $2$ hours together, so in one hour they can dig $\frac{1}{2}$ $1/2$ of the garden.

Benny alone can dig the garden in $5$ $5$ hours, so in one hour she can dig $\frac{1}{5}$ $1/5$ of the garden.

Hence in one hour Alyssa alone can dig $\frac{1}{2} - \frac{1}{5}$ $1/2-1/5$ of the garden.

or $\frac{5 \times 1}{5 \times 2} - \frac{2 \times 1}{2 \times 5} = \frac{5}{10} - \frac{2}{10} = \frac{3}{10}$ $(5xx1)/(5xx2)-(2xx1)/(2xx5)=5/10-2/10=3/10$ of the garden.

As Alyssa can dig $\frac{3}{10}$ $3/10$ of the garden in one hour,

It will take $\frac{10}{3} = 3 \frac{1}{3}$ $10/3=3 1/3$ hours or $3$ $3$ hours and $20$ $20$ minutes for Alyssa to finish the job.

Please also refer to [Tom can clean the store in twelve hours. If Sandy helps, it takes them ten hours. Without help, how...](https://socratic.org/questions/tom-can-clean-the-store-in-twelve-hours-if-sandy-helps-it-takes-them-ten-hours-w) for a similar poblem to get better idea.

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Alyssa and Benny were able to dig a garden in 2 hours together. It takes Benny 5 hours to ﬁnish this job alone. Without help, how long would it take Alyssa to ﬁnish this job?

1 Answer

Explanation:

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