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
Shwetank Mauria
Apr 3, 2016

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

Explanation:

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

Benny alone can dig the garden in 5 hours, so in one hour she can dig 1/5 of the garden.

Hence in one hour Alyssa alone can dig 1/2-1/5 of the garden.

or (5xx1)/(5xx2)-(2xx1)/(2xx5)=5/10-2/10=3/10 of the garden.

As Alyssa can dig 3/10 of the garden in one hour,

It will take 10/3=3 1/3 hours or 3 hours and 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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