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A man has been arrested on suspicion of murder after a 32-year-old woman's body was found on the M20 in Ashford.
Serious crime detectives say the man, who handed himself into a north Kent police station yesterday, is currently in custody.
The London-bound M20 was shut for more than 20 hours after the body was found near junction 9 just after 6pm on Tuesday.
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It fully reopened just before 3pm yesterday afternoon.
Police were searching for the driver of a silver Nissan Qashqai before the man handed himself in yesterday.
Officers say the victim was from Kent, but are not saying where in the county she was from.
Detective Chief Inspector Richard Vickery said: "I would still like to hear from anyone who may have seen the silver Nissan Qashqai with registration number KY15 WWX on the M20 between 5.30pm and 6.30pm on Tuesday, February 20 2018.
"In addition, I would like to hear from motorists who have dashcam footage taken between 5.30pm and 6.30pm on Tuesday 20 February of the M20 London-bound carriageway between junctions 10 and 9.
"I would also ask motorists who used the M20 after 6pm on Tuesday to contact us if they believe they experienced anything unusual whilst driving and check their cars for signs of involvement in this incident.
"We do not underestimate the impact that closing this stretch of the motorway had on people and I would like to thank drivers who were delayed for their patience while we ensured that all evidence was collected before the motorway was reopened."
In a separate incident, the coastbound carriageway was also closed on the same section of motorway following a crash involving four cars and a lorry.
Anyone who saw anything unusual in the area between junctions 10 and 9 on Tuesday evening should contact the serious collision investigation unit on 01622 798538, quoting reference 20-0913.
Alternatively email sciu.td@kent.pnn.police.uk