Question

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?

Answer 1

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.