Grace take 2 minutes to tpye 100 words. Jenny takes 40 seconds longer. If they started typing at the same how many more words will Grace have typed than Jenny after 30 minutes

Answer 1

First, let's find out how many words Grace and Jenny can type in a given time.

1. Grace's typing speed:

   • Grace types 100 words in 2 minutes.
   • This means her typing speed is: \[ \frac{100 \text{ words}}{2 \text{ minutes}} = 50 \text{ words per minute} \]

2. Jenny's typing speed:

   • Jenny takes 40 seconds longer than Grace to type 100 words.
   • Grace takes 2 minutes (which is 120 seconds) to type 100 words. Therefore, Jenny takes: \[ 120 \text{ seconds} + 40 \text{ seconds} = 160 \text{ seconds} \]
   • Her typing speed is: \[ \frac{100 \text{ words}}{160 \text{ seconds}} = \frac{100 \text{ words}}{2.67 \text{ minutes}} \approx 37.5 \text{ words per minute} \]

3. Words typed by Grace in 30 minutes: \[ \text{Words by Grace} = 50 \text{ words/minute} \times 30 \text{ minutes} = 1500 \text{ words} \]

4. Words typed by Jenny in 30 minutes: \[ \text{Words by Jenny} = 37.5 \text{ words/minute} \times 30 \text{ minutes} = 1125 \text{ words} \]

5. Difference in words typed: \[ \text{Difference} = \text{Words by Grace} - \text{Words by Jenny} = 1500 - 1125 = 375 \text{ words} \]

Thus, after 30 minutes, Grace will have typed 375 more words than Jenny.