Ue can wash a car in 1 hour. steve can wash a car twice as fast as sue. how long will it take them to wash a car if they work together, but sue starts 30 minutes before steve?

The rate of Sue is 1 car per hour: 1 (c/h)

then the rate of Steve is 2 (c/h) , because Steve works faster, he can wash twice the number of cars, for the same amount of time.

Thus If Steve and Sue work together, they can wash 1 + 2 = 3 
(cars per hour).

That is, the rate of Steve and Sue working together, is 3 (c/h).
 
In the first 30 minutes, Sue washes half of the car.

The remaining half will be washed at a rate of 3 (c/h)

The main formula is Work = Time * Rate

where Work is washing (1/2)c, and rate is 3(c/h)

Time=Work/Rate = 

1/ 6 h =(1/6)*60 min = 10 min

10 min