Yes, your rewrite is acceptable.
As for your confusion, it looks like you might have a case of DAMS (Definite Article Meaning Syndrome, a relatively common affliction that often affects English learners. It's chief symptom is confusion, generally caused by the erroneous belief that definite articles are only used for things previously referred to and specified in a narrative or conversation).
However, there are other uses of the definite article – ones that don't seem to get as much attention in ESL classes. For example, the word “the” can also be used:
- to refer to things that are unique (The Mona Lisa hangs in the Louvre.)
- to make a generalized reference to something (Bob plays the piano.)
- with adjectives, to refer to a group of people (This is another tax break for the rich.)
- to indicate that there is enough of something (She will bake a pie, if she has the ingredients.)
In the passage you quote, the author elected to use the definite article to make a generalized reference to the flora and fauna of Africa: grassy woodlands, lions and tigers. The wording would only seem strange to someone afflicted with DAMS.
This is worth mentioning, too; under its entry for the, NOAD lists:
used with a singular noun to indicate that it represents a whole species or class : they placed the African elephant on their endangered list.
(Disclaimer: DAMS is an acronym I just made up for the purpose of this answer. It was intended to be humorous. However, this isn't the first time I've witnessed this confusion; I've encountered it several times on both ELL and ELU.)
An actual answer is a reply that answer the question instead of going around it. The actual answer is the correct reply.
Let's say a politician was bribed. I ask him "were you bribed?". If he says "my finances are none of your concern", that is not an answer to the question. If he says "No", that is an actual answer to the question, but a wrong one (a lie). If he says "Yes", that is the actual answer to the question (the truth).
Best Answer
"Time" with the definite article would signify a specific time, as in,
or Michael Jackson's famous song:
Even if "the time" is not followed by "when.....", it will normally be specified elsewhere in the text, or the speaker will allude to a specific time that the person s/he is speaking to would remember.
is a phrase that would be used when someone is being nostalgic, after mentioning which time(s) exactly that was/were (college years, or else).
Another option:
Here again, "the time" is defined as that specific stretch of time in which this person baked a cake.
Your examples just refer to the general passage of time, not to specific stretches of it. So no article is necessary.