The quad bike can be found behind the yellow door alongside the high-speed train tracks, as described in the main walkthrough.

Get on the bike and ride up and around the series of metal ramps.

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If you're good with the controls, you can just drive up and around and then jump the bike across the tracks, but I found it helps to first position the bike with the blue column on your right, so you're facing directly across the tracks toward the opening on the other side (as shown in the screenshot above).

Then hold the brake (same key as Sprint), rev the engine (by holding Action), and then release the brake for a speed boost...

...that will help you make the jump more easily.

As you sail over the tracks, another high-speed train passes below.

Maintain speed as you race up the sloping tunnel...

...and over the next deep pit filled with toxic goo. After you clear the pit, turn sharply to the right to avoid going over the edge into another pit.

Now carefully turn the bike...

...so the fenced opening is behind Lara.

Line up a jump across the toxic pit using the edge of the uneven cement ledge as a ramp, as shown above. Again, hold the brake, rev the engine, and release the brake to race up the ramp...

...and sail across the next pit into the opening ahead.

As you continue through the tunnel into the next area, keep to the middle of the tunnel...

...to avoid the burning barrel ahead on the right. Now you can either run over the orange-suited worker on the right side of the train, or dismount (Roll + Left/Right) and shoot him.

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