Given "u" varies inversely to "t" and when t=5, then u=25, find the value of: 1) u when t=50 2)t when u=10

Whenever two numbers vary whether it be inversely, jointly, directly, etc. there is always a constant value k to solve for.

u = k/t

the first info provides enough to solve for k.

25 = k/5
25*5 = k
125 = k

now you have the equation
u = 125/t

1.) when t = 50
u = 125/50
u = 5/2

2.) when u = 10
10 = 125/t
t = 125/10
t = 61/2