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Wiktionary
make headway

vb. (context idiomatic English) To progress; to move forward.

WordNet
make headway

v. obtain advantages, such as points, etc.; "The home team was gaining ground"; "After defeating the Knicks, the Blazers pulled ahead of the Lakers in the battle for the number-one playoff berth in the Western Conference" [syn: gain, advance, win, pull ahead, get ahead, gain ground] [ant: fall back]

Usage examples of "make headway".

It continued to make headway, but was trailing thick black smoke from a hole in its superstructure just above the waterline.

It has a new wheel on it that can be cranked by one man and can almost make headway upriver without sail.

Unable to make headway and maneuver into a position to fire a clear shot, the Union fleet, despite their overwhelming firepower, suffered a great handicap.

The windstorm had become so fierce that Khrest had to lean heavily against it to make headway.

Giordino could feel the beat of the engines increase as the ship began to make headway.

He snatched the oars again and tried to row upstream and, yes, it was possible to make headway against the current.