A secretary types 350 words in 5 minutes. At this rate, (a) how long will he take to type 490 words? (b) how many words can he type in half an hour
The Correct Answer and Explanation is:
Here are the solutions to the problem.
(a) It will take the secretary 7 minutes to type 490 words.
(b) The secretary can type 2100 words in half an hour.
Explanation
This problem revolves around the concept of a constant rate of work. The initial information provides a baseline for the secretary’s typing speed: 350 words in 5 minutes. To solve both parts of the question, the first and most crucial step is to determine this rate in a standard unit, which is typically words per minute (WPM).
Calculating the Unit Rate
The secretary’s typing speed can be found by dividing the total number of words typed by the time it took in minutes.
- Typing Rate = Total Words / Time in Minutes
- Typing Rate = 350 words / 5 minutes = 70 words per minute
This means the secretary consistently types at a speed of 70 words every minute. This unit rate is the foundation for solving the subsequent questions.
(a) Time to Type 490 Words
The first question asks for the time required to type a specific number of words (490). Using the calculated rate of 70 WPM, the time can be determined by dividing the target word count by the typing speed.
- Time = Total Words / Typing Rate
- Time = 490 words / 70 words per minute = 7 minutes
Therefore, at this constant rate, it will take the secretary 7 minutes to complete 490 words.
(b) Words Typed in Half an Hour
The second question asks for the total number of words that can be typed in a given time frame (half an hour). First, it is necessary to express this time in minutes to match the unit of the typing rate. Since one hour contains 60 minutes, half an hour is equal to 30 minutes.
To find the total words, multiply the typing rate by the total time in minutes.
- Total Words = Typing Rate × Time in Minutes
- Total Words = 70 words per minute × 30 minutes = 2100 words
Thus, in a span of half an hour, the secretary can produce 2100 words.thumb_upthumb_down
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