Havn't found any time cheat.
I can help you out with a general strategy though. As usual with these sorts of games it's usually practice and getting used to the routes that brings home the bacon in the end.

To pass this mission you have to be quick (like you didin't know that ), and since the clue is in the last car you must be quick in and out of the other cars prior to that one.

Here are a few other time saving tips:
At first, eneter the car from the passanger side and take off in the direction the car is facing.
At the thrd intersection (the T-crossing) turn right, continue forward until you must turn left. Turn right again at the next intersection and put pedal to the metal.
At this point you should be heading the same direction as the first car (check the map to make sure). Hopefully you'll be able to get a head on collision followed by some wall-ramming until he is out.
Then you need to find a new car within 12-15 seconds and go after the others, they should be close by.

Hopefully that helps in some way. Just keep on trying, once you get it it'll be super sweet.
Good Luck

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