Question

Pete can type 80 words in the same time that Ralph can type 50 words. If they type at those rates

for an extended period of time, when Ralph has typed 4000 words, how many words has Pete
typed?

Answer 1

When Ralph has typed 4000 words, Pete has typed 6400 words, based on their respective typing rates.

Step-by-step explanation:

The student's question involves a ratio word problem where Pete and Ralph have different typing speeds. Pete can type 80 words in the same time Ralph types 50 words. To calculate how many words Pete has typed when Ralph has typed 4000 words, you divide Ralph's total words by his rate and then multiply by Pete's rate. The rates form a ratio of Pete's words to Ralph's words, which is 80:50 or simplified to 8:5.

First, determine the amount of time Ralph takes to type 4000 words. Since Ralph types 50 words in some unit of time, we can use this rate to find how many units of time it takes for him to type 4000 words: 4000 words ÷ 50 words/unit of time = 80 units of time.

Next, use the time to calculate how many words Pete can type in the same period: 80 units of time × 80 words/unit of time = 6400 words. So, when Ralph has typed 4000 words, Pete has typed 6400 words.

Answer 2

After the extended period of time, Pete would have typed 6400 words.

Step-by-step explanation:

Given the data in the question;

In the same time;

number typed word of Pete = 80

type word of Ralph = 50

After a period time;

number of typed word of Pete = ?

number of typed word of Ralph = 4000

so, let x represent the number of typed word by Pete after an extended period.

so

80 words = 50 words

x words = 4000 words

we cross multiply

x × 50 = 4000 × 80

x = ( 4000 × 80 ) / 50

x = 320000 / 80

x = 6400

Therefore, After the extended period of time, Pete would have typed 6400 words.