が早(はや)いかno sooner ... than ..., hardly ... when ..., as soon as

病院(びょういん)から知(し)らせを受(う)けるが早(はや)いか家(いえ)を飛(と)び出(だ)した。

As soon as I received the news from the hospital, I dashed out of the house.

犬(いぬ)はお散歩(さんぽ)と聞(き)くが早(はや)いか、リードを持(も)ってきました。

As soon as the dog heard 'walk', it brought the leash.

テストを返却(へんきゃく)されるが早(はや)いか、彼(かれ)は解(と)き直(なお)しを始(はじ)めました。

As soon as the test was returned, he started reworking the problems.

喧嘩(けんか)を売(う)られるが早(はや)いか、武闘(ぶとう)派(は)の彼(かれ)は相手(あいて)を殴(なぐ)り始(はじ)めました。

As soon as a fight was picked with him, the brawler started hitting the other guy.

お腹(なか)が空(す)いていて、ご飯(はん)を出(だ)されるが早(はや)いかガツガツ食(た)べてしまいました。

When I was hungry, as soon as the food was served, I devoured it voraciously.