# SOLUTION: If Steven can mix 20 drinks in 5 mins., Sue can mix 20 drinks in 10 mins., and Jack can mix 20 drinks in 15 mins, how much time will it take all 3 of them working together to mix t

Algebra ->  Algebra  -> Rate-of-work-word-problems -> SOLUTION: If Steven can mix 20 drinks in 5 mins., Sue can mix 20 drinks in 10 mins., and Jack can mix 20 drinks in 15 mins, how much time will it take all 3 of them working together to mix t      Log On

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 Click here to see ALL problems on Rate-of-work-word-problems Question 73619: If Steven can mix 20 drinks in 5 mins., Sue can mix 20 drinks in 10 mins., and Jack can mix 20 drinks in 15 mins, how much time will it take all 3 of them working together to mix the 20 drinks?Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!Steven mixes 20 drinks in 5 minutes. Therefore, he mixes 4 drinks per minute. (Get this by dividing 5 into 20.) . Sue mixes 20 drinks in 10 minutes. Therefore, she mixes 2 drinks per minute. . Jack mixes 20 drinks in 15 minutes. Therefore, he mixes drinks per minute. . The problem implies that they all start mixing drinks at the same time. Therefore in mixing drinks they all work the same time t. And we need to know when they reach 20 drinks total. . In equation form we multiply their individual mixing rates by the time t to get: . . Factor the t out on the left side: . . Putting all the numbers in the parentheses over the common denominator of 3 results in: . . Combine all the fractions by adding their numerators and placing them over the common denominator of 3 to get: . . Solve this problem by dividing both sides by . On the left side this just leaves t. On the right side, recall the rule that dividing by a fraction is the same as multiplying by its inverse. Therefore, the right side can be determined by multiplying: . . Take your calculator and divide 30 by ll to find that . So the answer is minutes. And 0.727 times 60 seconds is about 43.6 seconds. So the answer to this problem is t = 2 minutes and 43.6 seconds. . Hope this helps you to think your way through the problem.