SOLUTION: Two harvesting machines can each harvest a field in 15 hrs. If they are joined by a newer machine and the three machines work together, the job takes 3 hrs. How long would it talk
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Question 121892This question is from textbook
: Two harvesting machines can each harvest a field in 15 hrs. If they are joined by a newer machine and the three machines work together, the job takes 3 hrs. How long would it talk for the newer machine to harvest the field alone?
i have not a clue where to start...im so bad at story problems..i can do the problems and get algebra but i never know what to do with story problems and how to set them up?
This question is from textbook
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two harvesting machines can each harvest a field in 15 hrs. If they are joined by a newer machine and the three machines work together, the job takes 3 hrs. How long would it take for the newer machine to harvest the field alone?
:
Let x = the time the newer machine needs to complete the job alone
Let the completed job = 1
:
Each machine will do a fraction of the work
All three will work for 3 hrs so we can say:
Each original machine will 3/15
The new machine: 3/x
Remember the completed job = 1:
:
+ + = 1
:
we can simplify this the 1st two machine = 6/15 reduced to 2/5
:
Now we have a real simple equation:
+ = 1
:
Multiply the equation by 5x to get rid of the denominators
5x* + 5x = 5x(1)
:
Cancel out the denominators and we have:
2x + 15 = 5x
15 = 5x = 2x
15 = 3x
x =
x = 5 hrs for the new machine to do it alone.
:
:
Check solution in the original equation
3/15 + 3/15 + 3/5 =
1/5 + 1/5 + 3/5 = 1; confirms our solution
:
:
Hopefully this provided a few clues, did it make sense to you? Any questions?
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