Calculating P(U-3 < 4.33 sqrtV) Using t Distribution

[dim&dimmer]

t distribution??

Homework Statement

If U and V are independent, U being distributed N(3,16) and V being distributed as chi-square on 9 degrees of freedom, find

P(U-3 < 4.33 sqrtV).

Homework Equations

The Attempt at a Solution

Well I don't even know where to start! Does U-3 suggest the mean is 0? Is the whole distribution of U shifted left by 3? Does that give a t distribution?
I am not asking for the answer but some direction would be appreciated, I just can't seem to understand this at all.

 

[EnumaElish]

U-3 is distributed N(0,16).

 

[dim&dimmer]

Ok, I understand this and also can reason that the probability would be very high, just by thinking of the graphs of the distributions, however I am still at a loss as to how to compute the probability. I use R to do the calculations, is it some kind of t test or do I put in the distributions and their parameters and just use R to calculate the probability, if so... is the R code just the same as in the question, that is, P(U-3 < 4.33 sqrtV)