Problem Solving

I must be missing a point with the work problems, b/c I keep missing all of them.

Five farm workers can pick 10 acres of blueberries in 20 hours. How many hours would it take 8 workers to pick the same amount of blueberries?

A. 12.5
B. 14
C. 16
D. 23
E. 32

OA is A

Since the amount is the same, we need to find how long does it take 1 worker: 5 workers - 20 hours, so 1 worker - 4 hours. Then it would take 32 hours for 8 workers?

Please explain. Thanks.

5 workers pick 10 acres of blueberry fields in 20 hours

1 worker can pick 2 acres of blueberry fields in 20 hrs.

1 worker can pick 1/10 (2/20) acres of blueberry fields in 1 hr.

8 workers can pick 4/5 (8/10) acres of blueberry fields in 1 hr.

8 workers can pick 10 (4/5)*(25/2) acres of blueberry fields in 25/2 hrs.

So total time it takes to pick for 8 workers in 10 acres is: 25/2 = 12.5hrs.

oks wrote:I must be missing a point with the work problems, b/c I keep missing all of them.

Five farm workers can pick 10 acres of blueberries in 20 hours. How many hours would it take 8 workers to pick the same amount of blueberries?

A. 12.5
B. 14
C. 16
D. 23
E. 32

OA is A

Since the amount is the same, we need to find how long does it take 1 worker: 5 workers - 20 hours, so 1 worker - 4 hours. Then it would take 32 hours for 8 workers?

Please explain. Thanks.

You know i used to face the same confusion in work, but if u like i can just clear a basic funda of yours which would always help you. Just remember in work its usually inverse variation instead of direct. You can always check it with logic, like here since 5 people take 20 hrs so it would be obvious that more ppl will take less than 20 hours right?
so now just plug in the equation but inverse variation.
i.e
lets assume the no. of hrs required to be x
so,
5/8=x/20
now solving for x you'll get x=12.5

oh and one more thing , here it formed a simple inverse equation, because 10 acres was constant, else you would have to first calculate for a constant amount and then vary, had 10 acres changed to something else.

Work problem is my concern, too.
I found an easier way to approach this kind of problem.
If it takes M workers H hours to finish a job, then each worker does 1/MH of the job in an hour. So the rate of each worker is 1/MH.
----------------------
Apply this to your problem: Five farm workers can pick 10 acres of blueberries in 20 hours. So the rate of each worker is 1/(5*20)=1/100.
8 workers will do 8*1/100=8/100 of the job in an hour.
Call T is the time it takes 8 workers to complete the job (1 job).
Then (8/100)(T)=1 => T=100/8=12.5

hey u can use the allegation method too:

5 x


8 20

5*20=8*x
x=12.5

since you are keeping the "10 acres" constant . . . there is an easier way to do this.

5 workers__________10 acres___________20hours

1 worker___________10 acres___________100 hours

so . . . if it takes 1 worker 100 hours, it would take eight workers, 100/8 = 12.5