WORD PROBLEMS

Question

Three postal workers can sort a stack of mail in 20 minutes, 25 minutes, and 100 minutes, respectively. Find how long it takes them to sort the mail if all three work together.

Answer 1

Tracey's answer is absolutely correct.  Just as another way to look at it though:

 

The three workers are all working together - The below equation is a way to quickly determine how long it takes when they work "in parallel":

 

1/20 + 1/25 + 1/100 = 1/T

 

Solve for T, and you get T=10.  The time is 10 minutes.

Answer 2

These problems stumped me in high school but I enjoy working them now.

 

The first worker can sort the stack in 20 minutes. So every minute that goes by, he does 1/20 of the job.

 

Likewise, for every minute, the second worker does 1/25 of the stack and the third does 1/100 of the job per minute.

 

The question is how many minutes will it take if they all work together. Set up an equation that shows what they accomplish each minute.

 

x stands for minutes and I'm setting it all equal to 1 because this represents that 1 entire stack was sorted.

 

x·1/20 + x·1/25 + x·1/100 = 1

 

Multiply each term by 100 to clear the equation of all fractions

 

100x/20 + 100x/25 + 100x/100 = 100

 

5x + 4x + 1x = 100

 

10x = 100

x = 10

 

The answer is 10 minutes