# If sylvia types at 45 wpm she can finish her work in 4 hours. How long will it take her if she types at: a) 30 wpm b) 60 wpm c) 45 wpm and she has a friend who helps her type at 30 wpm

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If it takes Sylvia 4 hours to do her work at 45 wpm, we can figure out how many words` ` she has to type by multiplying 45 by 60 to convert the rate to words per hour. Then we multiply the rate (2700 wph) by the 4 hours to get an assignment total of 10,800 words.

To find how long it will take to finish at 30 wpm, you divide the assignment 10,800 by the rate and that gives you the minutes and then divide by 60 to get 6 hours. `10,800-:30=360 min.` and `360-:60=6`

To find at 60 wpm we do the same thing, using 60 instead of 30. `10,800-:60=180` and `180-:60=3` So it will take 3 hours, which is logical, half the time at twice the speed.

To find the combined times of Sylvia going 45 wpm, and her friend at 30, requires a little algebra. We know that the assignment is 10,800 words. If we multiply each workers rate of typing by t minutes and add them together, we will find how many minutes it will take them together to type 10,800 words. Then we divide t by 60 to find hours if appropriate. `45t+30t=10,800->75t=10,800->t=10,800-:75=144` and `144-:60=` 2hrs 24min.

typing speed more ,work finish in less time.

typing speed less ,work finish in more time.

(i) wpm 45 work finish in 4 hours.

**wpm 30 work finsh =`(45xx4)/30=6` hours.**

(ii) **wpm 60 ,work finish =`(45xx4)/60=3 ` hours**.

(iii) **Sylvia's friends typing speed is 30 wpm mean she can finsh work ****in 6 hours. ( just part (i))**

Sylvia ,wpm 45 then she can finsh work in 1 hour= 1/4

Sylvia"s freinds wpm 30 then she can finsh work in i hour= 1/6

When both worked together can finsh work in 1 hour=`1/4+1/6`

`=5/12`

**Thus worknig together can finsh work in `12/5` hours**.