They created 31.25 slides per hour, 31 and a quarter
See the attached sketch. Let
denote angle ABC and
denote angle CBD. Then
.
From the sketch, we see that


Write
in terms of
. Recall the angle sum identity for tangent:

This gives us

and plugging in
leaves us with

and so AD = 5 * 37/55 = 37/11.
The square root of x equals ten is 5