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 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

D. 5

12 - 7 = 5

just shoot the answer . i dont know actually

Explanation:

List out the multiples of each number until we find the LCM

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.

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 84-17x 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 84-17x items at a rate of 10 items per hour. The time span they have left is 7-x hours.

This means we can form the following equation

(84-17x)/(10) = 7-x

Divide the number of items over the unit rate to find the time duration in hours.

Solve for x

(84-17x)/(10) = 7-x

84-17x = 10(7-x)

84-17x = 70-10x

84-70 = -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 84-34 = 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.

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: