It takes A 12 hours alone, B 14 hours alone, and C 21 hours alone to move the goods in a warehouse. The three of them work together at the beginning, but A left
Question
hours alone, and C 21 hours alone
to move the goods in a
warehouse. The three of them
work together at the beginning,
but A left in the middle of the
day.
It took a total of 7 hours for
them to finish.How many hours
did A work?
PLEASE HELP MY TEACHER WANTS THE WORK AND THIS IS WORTH HALF OUR GRADES1
A. 1
B. 2
C. 4
D. 5
2 Answer
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1. User Answers ftnrsyfqh02
Answer:
D. 5
12  7 = 5
just shoot the answer . i dont know actually

2. User Answers jimthompson5910
Answer: B) 2
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Explanation:
List out the multiples of each number until we find the LCM
 multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, ...
 multiples of 14 are: 14, 28, 42, 56, 70, 84, 98, ...
 multiples of 21 are: 21, 42, 63, 84, 105, ...
We see that 84 shows up in the list and it is the smallest such common item. The LCM of the numbers {12,14,21} is 84.

Let's say there are 84 items to be moved in the warehouse.
 If person A works alone, then their unit rate is 84/12 = 7 items per hour
 If person B works alone, then their unit rate is 84/14 = 6 items per hour
 If person C works alone, then their unit rate is 84/21 = 4 items per hour
We divide 84 over the respective time values given by your teacher, to find each unit rate.
Let x be the the length of time (in hours) that person A worked. They work alongside persons B and C to get a combined unit rate of 7+6+4 = 17 items per hour. This assumes no worker gets in the way of any others. They work the most efficiently together.
After x hours, they manage to move 17x items in the warehouse.
After x hours are up, there are 8417x items left to move. Person A leaves B and C to finish up, so B and C's combined rate is 6+4 = 10 items per hour. These two remaining people move the 8417x items at a rate of 10 items per hour. The time span they have left is 7x hours.
This means we can form the following equation
(8417x)/(10) = 7x
Divide the number of items over the unit rate to find the time duration in hours.

Solve for x
(8417x)/(10) = 7x
8417x = 10(7x)
8417x = 7010x
8470 = 10x+17x
14 = 7x
7x = 14
x = 14/7
x = 2
Person A works for 2 hours

If person A worked for 2 hours, then persons A,B,C moved 17*2 = 34 items. This leaves 8434 = 50 items left. Person A takes off to leave persons B and C to handle the rest of the job. These two remaining people have a combined rate of 10 items per hour. So they take 50/10 = 5 hours when person A leaves. That gives the 2+5 = 7 hours total. This confirms the correct answer.