A fast typist can type 120 words in 100 seconds. At that rate, how many seconds would it take to type 258 words?

To solve this, we can use the concept of proportionality. The typist's rate is constant, so the ratio of words typed to time taken will remain the same.

First, find the rate of typing in words per second:

\[
\text{Rate} = \frac{120 \text{ words}}{100 \text{ seconds}} = 1.2 \text{ words/second}
\]

Now, we need to find how much time it would take to type 258 words. Let \( t \) represent the time in seconds:

\[
t = \frac{258 \text{ words}}{1.2 \text{ words/second}} = 215 \text{ seconds}
\]

Therefore, it would take the typist **215 seconds** to type 258 words.

Would you like further clarification or more details?

Here are 5 related questions for practice:
1. If the typist improves their speed to 150 words in 100 seconds, how long would it take them to type 300 words?
2. How many words can the typist type in 60 seconds at their original speed?
3. If another typist types 200 words in 150 seconds, who is faster?
4. What is the typing speed in words per minute for the typist?
5. How many words can the typist type in 5 minutes at their current rate?

**Tip**: When dealing with constant rates, use the formula: \( \text{Rate} = \frac{\text{Distance or Amount}}{\text{Time}} \). This helps in both speed and efficiency problems.

Find out how long it would take a typist to type 258 words at a rate of 1.2 words per second. This problem uses proportionality and rate formulas to calculate the time. Ideal for students in Grades 6-8 learning about rates and proportionality.

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