Fast, slow, properly, well
Everyday manner adverbs that go straight before a verb to say how it's done: speed, care, and whether it works.
hayaku
quickly; early; hurry up
早く はやく
The adverb form of hayai: before any verb it means fast or early (hayaku kaeru, hayaku okiru), and 'hayaku!' on its own means hurry up.
hayaku shite ne.
Be quick, okay?
早くしてね。
hayaku shite kudasai ne.
Please be quick.
早くしてくださいね。
Spoken hayaku covers both 早く (early) and 速く (fast); the sound is the same. To a clerk or coworker, hayaku shite kudasai sounds impatient, so soften it: sumimasen, chotto isoide iru n desu ga... (sorry, I'm in a bit of a hurry).
yukkuri
slowly; take your time
ゆっくり
A manner adverb for slow, unhurried action: yukkuri de ii (yo) means no rush, take your time, and mou sukoshi yukkuri asks someone to slow down. yukkuri shite ne / yukkuri shitette ne is different: a host's 'relax, make yourself at home'.
yukkuri de ii yo.
No rush, take your time.
ゆっくりでいいよ。
yukkuri de ii desu yo.
No rush, take your time.
ゆっくりでいいですよ。
Survival line: mou sukoshi yukkuri hanashite kudasai (please speak a little more slowly), or simply yukkuri onegaishimasu. goyukkuri douzo (enjoy, take your time) is the shop and host set phrase.
Learn alongside: hayaku
chanto
properly; as one should
ちゃんと
Says something is done the right, responsible way (chanto tabete, chanto kiite), and 'chanto shita hito' is a proper, reliable person.
chanto tabete ne.
Make sure you eat properly.
ちゃんと食べてね。
chanto tabete kudasai ne.
Please make sure you eat properly.
ちゃんと食べてくださいね。
kichinto is a stiffer synonym. chanto is fine in polite speech too.
umaku
well; smoothly
うまく
Says something works out or is done skilfully. It is used mostly in 'umaku iku' (go well) and in negatives that describe trouble (umaku ienai = can't put it well).
shiken, umaku itta?
Did the exam go well?
試験、うまくいった？
shiken, umaku ikimashita ka?
Did the exam go well?
試験、うまくいきましたか？
Learner lifeline: umaku ienai kedo... (I can't put it well, but...).
Learn first: iku