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Question 146242: If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, 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 minutes and 44 seconds
B. 2 minutes and 58 seconds
C. 3 minutes and 10 seconds
D. 3 minutes and 26 seconds
E. 4 minutes and 15 seconds
Found 3 solutions by Earlsdon, scott8148, oberobic:
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let's find the rate (per minute) of each person can do the job (mix 20 drinks).
If Steven can do the job (mix 20 drinks) in 5 minutes, then he can do 1/5 of the job in 1 minute.
If Susan can do the job (mix 20 drinks) in 10 minutes, then she can do 1/10 of the job in 1 minute.
If Jack can do the job (mix 20 drinks) in 15 minutes, then he can do 1/15 of the job in 1 minute.
Together, the three of them can do (1/5 + 1/10 + 1/15) of the job in 1 minute.
So if the three of them can do 11/30 of the job in 1 minute, then it takes them 30/11 minutes to do the whole job (mix 20 drinks).
 minutes or 2 mins 44 secs.
Answer by scott8148(6628)  (Show Source):
You can put this solution on YOUR website! a person working with a group does some fraction of the whole task
__ this fraction is the group time divided by the individual time
eg. Bob can do a task in 6 hrs __ if it takes the group 2 hrs to do the task then Bob does 2/6 or 1/3 of the task
__ the individual fractions add to 1 (the whole task)
let x=group time __ x/5+x/10+x/15=1 __ multiplying by 30 (LCM) __ 6x+3x+2x=30 __ 11x=30 __ x=30/11 min
answer A looks like a winner
Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website! This work problem is similar to a mixture problem. Looking at the work done by each person, you can see that Steve can do the entire job in 5 minutes (given), Sue can do it in 10 minutes (given), and Jack can do it in 15 minutes (also given).
Converting each person's work to "drinks/minute," you see that Steve can mix 4 drinks per minute (20 drinks/5 min); Sue can mix 2 drinks per minute (20/10); and Jack can mix 1.33 drinks per minute (20/15). Working together they can mix 7.33 drinks per minute (4 + 2 + 1.33).
So, how many minutes does it take to mix 20 drinks?
7.33x = 20
, where 7.33 is the combined drinks/minute and x is the unknown number of minutes; 20 is the desired number of drinks.
Dividing through by 7.33, we have
x = 20/7.33 = 2.73 minutes
Since the required answer is in minutes and seconds, we have to multiply .73 minutes by 60 seconds per minute to get the seconds, which equals 43.8 or about 44 seconds.
So the answer in the required format is 2 minutes and 44 seconds.
ALWAYS CHECK YOUR WORK!
How many drinks does Steve make in 2.73 minutes? Just multiply by his rate, which is 4/minute: 2.73 * 4 = 10.92
How many drinks does Sue make in 2.73 minutes? Multiply by her rate, which is 2/minute: 2.73 * 2 = 5.46
How many drinks does Jack make in 2.73 minutes? Multiply by his rate, which is 1.33: 2.73 * 1.33 = 3.63.
Adding up: 10.92 + 5.46 + 3.63 = about 20 drinks (more or less).
Of course, in the real world, .92 of a drink or .46 of a drink or .63 of a drink is nonsensical: You either have a drink or you don't. But for our algebraic purposes, we have an answer. (smile)
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