Hint: The last letter should be N.

Answer: Lemon.

 LATE
NET
 MIME
POACH
 NEAR

Hint: How many baths could the cold tap fill?

Answer: 45 minutes.

In 24 hours:
   the cold tap could fill 80 baths
   the hot tap could fill 96 baths
   the plug could drain 144 baths

Therefore, in 24 hours, we have 80 + 96 - 144 baths full = 32 baths.

Therefore each bath would take 45 minutes to fill.

Hint: Start by filling the 11 gallon container.

Answer: Here are the contents of the containers after each stage:

A      B
0      11          fill B
7      4           fill A from B
0      4           empty A
4      0           fill A from B
4      11          fill B
7      8           fill A from B
0      8           empty A
7      1           fill A from B
0      1           empty A
1      0           fill A from B
1      11          fill B
7      5           fill A from B
0      5           empty A
5      0           fill A from B
5      11          fill B
7      9           fill A from B
0      9           empty A

This leaves 9 gallons in container B.

Hint: Say what you see.

Answer: Tent: Ten T.

Hint: Every word must contain the central letter.

Answer:
Common words: ache, aches, arch, archer, archers, arches, ash, ashore, cash, chaos, char, chart, charter, charters, charts, chase, chaser, chaste, chat, chats, cheat, cheats, chest, chore, chores, chose, crash, each, earshot, earth, echo, etch, hare, hares, has, haste, hat, hate, hates, hats, he, hear, hears, heart, hearts, heat, heats, her, hero, hers, hoarse, hoarser, horse, hose, host, hot, oath, oaths, ORCHESTRA, other, others, rash, rasher, rather, reach, retch, roach, roaches, sachet, scathe, search, share, she, shear, shoe, shore, short, shorter, shot, starch, teach, the, theca, those, torch, torches, trash

All words: ache, aches, ah, ahorse, arch, archer, archers, arches, ash, ashore, cash, chao, chaos, char, chare, chares, charr, charro, charros, charrs, chars, chart, charter, charters, charts, chase, chaser, chaste, chaster, chat, chats, cheat, cheats, chert, cherts, chest, chore, chorea, choreas, chores, chose, cosh, cosher, crash, crasher, each, earshot, earth, earths, eath, echo, echos, eh, eschar, etch, eth, ethos, eths, ha, hae, haes, haet, haets, hao, hare, hares, hart, harts, has, hast, haste, hat, hate, hater, haters, hates, hats, he, hear, hears, heart, hearts, heat, heats, hector, hectors, her, hero, heros, hers, hes, hest, het, hets, ho, hoarse, hoarser, hora, horas, horse, horsecar, horst, horste, hose, host, hosta, hot, hots, oath, oaths, ocher, ochers, ochre, ochrea, ochres, oh, ohs, orach, orache, oraches, ORCHESTRA, other, others, rachet, rachets, rah, rash, rasher, ratch, ratches, rath, rathe, rather, reach, rechart, recharts, resh, reshot, retch, rhea, rheas, rhetor, rhetors, rho, rhos, roach, roaches, rochet, rochets, rotch, rotche, rotches, sachet, scathe, search, sh, sha, share, sharer, she, shea, shear, shoat, shoe, shoer, shore, short, shorter, shot, shote, soth, starch, tach, tache, taches, tachs, tahr, tahrs, teach, thae, the, theca, tho, thoraces, those, thro, throe, throes, tocher, tochers, torah, torahs, torch, torches, tosh, trash, trochar, trochars, troche, troches.