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Liam can type faster than any of his classmates. He took a test that showed he can type 700 words in 5 minutes. At this rate, how long does Liam need to type a 20 -page paper with 250 words on each page? Round your answer to the nearest whole minute.

Liam can type faster than any of his classmates. He took a test that showed he can type $700$ words in $5$ minutes. At this rate, how long does Liam need to type a $20$ -page paper with $250$ words on each page? Round your answer to the nearest whole minute.

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Exponential growth and decay: word problems

Full solution

Q. Liam can type faster than any of his classmates. He took a test that showed he can type

700

words in

5

minutes. At this rate, how long does Liam need to type a

20

-page paper with

250

words on each page? Round your answer to the nearest whole minute.

Calculate Total Number of Words: Calculate the total number of words in the $20$ -page paper. $\newline$ Reasoning: Multiply the number of pages by the number of words per page to get the total number of words. $\newline$ Calculation: $20$ pages $\times$ $250$ words/page $=$ $5,000$ words $\newline$ Math error check:
Calculate Time per Word: Calculate the number of minutes Liam takes to type one word. $\newline$ Reasoning: Divide the time taken to type a certain number of words by that number of words to find the time per word. $\newline$ Calculation: $5$ minutes $\div$ $700$ words = $0.00714$ minutes/word (rounded to $5$ decimal places) $\newline$ Math error check:
Calculate Total Time: Calculate the total time Liam needs to type the $20$ -page paper. $\newline$ Reasoning: Multiply the time it takes to type one word by the total number of words in the paper. $\newline$ Calculation: $0.00714$ minutes/word $\times 5,000$ words = $35.7$ minutes $\newline$ Math error check:
Round Total Time: Round the total time to the nearest whole minute. $\newline$ Reasoning: Since we are asked to round the answer, we look at the decimal part of the time calculated. If it's $0.5$ or higher, we round up. If it's lower than $0.5$ , we round down. $\newline$ Calculation: $35.7$ minutes rounds up to $36$ minutes because $0.7$ is greater than $0.5$ . $\newline$ Math error check:

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