The phrase "are distracted with" is correct and usable in written English.
It can be used when describing a state of being unable to concentrate due to various factors or stimuli.
Example: "The students are distracted with their phones during the lecture."
Alternatives: "are preoccupied with" or "are sidetracked by".
"That is something that the Bush administration doesn't want to do because we are distracted with Iraq and want to pick our fights, but the North Koreans are giving us no choice".
And the critics point out that big mergers in the fast-moving computer business nearly always fail, as the two enterprises are distracted with internal matters as markets and rivals move ahead.
To maintain morale, the customers are distracted with dioramas -- cuddly George Lucas androids repairing spaceships at the Star Tours simulation, a nifty African Queen set for the Jungle Cruise.
There isn't necessarily less inventory available at that time; it's just that most people are distracted with the holidays".
(Really? Apparently, as with recorded programs on DVRs, Hulu viewers must forget they have the option, or are distracted with other things).
While Yahoo and AOL are distracted with firing people and integrating business units and backend technologies for at least two years, the Internet will continue to move ahead without them.
After a latency period of 7 days, the bone segment was distracted with a distraction rate of 1 ml, per day in four 0.25 mm increments.
Meg will be distracted with McCain for the next six months; we should jump early on insider stuff".
Half of the group was left to think over the choices; the other half was distracted with word puzzles.
"He was very adamant that we stay tightly focused on videogames, without being distracted with other 'leverage opportunities'".
They had hopes, too, that Saints might be distracted, with a crucial game at West Bromwich on Tuesday.
