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... for a similar poblem to get better idea.