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i need some math help please? not sure how to work it out?

If steven can mic 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 mintues, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

a) 2 min and 44 sec

b) 2 min and 58 sec

c) 3 min and 10 sec

d) 3 min and 26 sec

e) 4 min and 15 sec

help please??

Answers (2)

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So,

Steve takes 15 seconds per drink

Sue takes 30 secs per drink

Jack takes 45 secs per drink

After the first 90 seconds, they have made 6+3+2=11 drinks and are all starting a new drink.

Another 75 seconds and Steve has made 5 more, Sue has made 2 more, and Jack has made 1 more. Still only 19 drinks!

So, We need another 15 seconds. No drinks can be made in less than 15 seconds. The algebraic solution doesn't work, since drinks are either finished or not. Fractional drinks cannot be mixed by two bartenders then poured together to save time.

After 180 seconds (3 minutes), we have 22 drinks.

They all finished those last three at the same time. So, 20 for the customers and 2 left over for us!!!