SOLUTION: How do i solve a problem like this? If it takes 8 workers 3 hours to clean 2 miles of highway, how long would it take 15 workers to clean 8 miles of highway?

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Question 851768: How do i solve a problem like this? If it takes 8 workers 3 hours to clean 2 miles of highway, how long would it take 15 workers to clean 8 miles of highway?
Found 2 solutions by Edwin McCravy, josgarithmetic:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
How do i solve a problem like this? If it takes 8 workers 3 hours to clean 2 miles of highway, how long would it take 15 workers to clean 8 miles of highway.
Use the worker-time-job formula, which is:

%28W%5B1%5DT%5B1%5D%29%2FJ%5B1%5D%22%22=%22%22%28W%5B2%5DT%5B2%5D%29%2FJ%5B2%5D

where

W1 = the number of workers in the first situation.
T1 = the number of time units (hours in this case) in the first situation.
J1 = the number of jobs in the first situation. (a "job" is
"a highway mile "hwm" cleaned")

W2 = the number of workers in the second situation.
T2 = the number of time units (hours in this case) in the second situation.
J2 = the number of jobs in the second situation.  (a "job" is
"a highway mile "hwm" cleaned")


W1 =  8             W2 = 15     
T1 =  3 hrs         T2 = The unknown quantity 
J1 = 2 hwm          J2 = 8 hwm

%28W%5B1%5DT%5B1%5D%29%2FJ%5B1%5D%22%22=%22%22%28W%5B2%5DT%5B2%5D%29%2FJ%5B2%5D

%288%2A3%29%2F2%22%22=%22%22%2815%2AT%5B2%5D%29%2F8

24%2F2%22%22=%22%22%2815%2AT%5B2%5D%29%2F8

Cross-multiply

30T2 = 192

Divide both sides by 30

T2 = 192%2F30 = 6.4 hours

0.4 hours = 24 minutes

Answer: 6 hours 24 minutes.

Edwin

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform rates, work problem. R*T=J, rate, time, amount of job.
How long does it take 1 worker to the the job if alone?

8 workers: Let's cut that down to 1 mile of highway.
8 workers do 1 mile of highway in 3%2F2 hours.
Let us define the job as "clean 1 mile of highway".

-
WHAT IS THIS RATE FOR 1 WORKER? Eight Times Longer.
1 worker needs 8%283%2F2%29 hours to do 1 job alone. This is 8%283%2F2%29=12 hours.
-
One-worker rate is highlight%281%2F12%29 JOBS per HOUR.

Now, you want 15 workers and you want time to be t, a variable, and you want J=8 miles of highway. Remember, this solution is using the job as "clean 1 mile of highway".
-
highlight%2815%281%2F12%29t=8%29------If this makes sense, then you are understanding; otherwise, you are stuck until it does make sense.

t=8%281%2F15%29%2812%2F1%29 hours
t=%282%2A2%2A2%2A4%2A3%29%2F%2815%29
t=2%2A2%2A2%2A4%2F5
t=32%2F5
highlight%28t=6%264%2F5%29 hours