Does an open mri take longer than a closed mri?

Its a bit like comparing Apples and Pears! Older instruments are closed some could only take patients upto 140kg and not many were big enough to allow most head restraints used by surgeons. Open imagers were designed to make the experience less clostrophobic and allow larger object to be placed inside.

If you were performing the same tests then the time difference is probably non-existant for a modern open and a modern closed instrument. However, you are probably comparing an old closed instrument with a modern open instrument - the open is quicker. However, if the hospital has been diligent enough to buy a modern instrument perhaps they would like to run more tests whilst you are in the MRI scanner. Each test is run separetly and so running more tests with the instrument in different modes will take longer. Your radiographer will be able to tell you exactly how long the scan will take.

Summary - Open instruments tend to be more modern than closed instruments. Open instruments are more plesant to be scanned in. The number of modes of scan performed it the critical factor in how long the scan takes.