Company x can install chairs in a theater in 10 hours. company y can install them in 15 hours. the owner of the theater wants the chairs installed in less than one day (8 hours). if the two companies work together, can they install the chairs in less than one day?

Yes, they can install chairs in less than one day

Explanation:
1- For company X:
They can install the chairs in 10 hours
This means that:
in 1 hour, company X would have finished 1/10 of the work required

2- For company Y:
They can install the chairs in 15 hours
This means that:
in 1 hour, company Y would have finished 1/15 of the work required

Now, we will calculated the fraction of work that will be finished in one hour if the two companies worked together:
fraction of work = fraction finished by X + fraction finished by Y
fraction of work = 1/10 + 1/15
fraction of work = 1/6

This means that:
In one hour, 1/6 of the work would be finished
which means that the two companies would need 6 hours to finish the entire work

It's obvious that 6 hours is less than one day.
Therefore, the answer is YES.

Hope this helps :)