SOLUTION: Farmers mowed 60 acres of grass a day instead of 50 and managed to finish the task one day earlier than planned. What is the area of the meadow they were mowing?

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Question 1055859: Farmers mowed 60 acres of grass a day instead of 50 and managed to finish the task one day earlier than planned. What is the area of the meadow they were mowing?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Work Rates Description.
RT=J relates rate, time, amount of jobs or amount of job. The example uses rate unit of acres per day.

Use the description and rate rule to fill a data table. 
                   RATE           TIME         JOB

DONE                60            t-1           1

PLANNED             50             t            1

"The task", is 1 whole job, and that is what the description discusses. We do not know how many acres is in ONE JOB, but we know that the DONE and the PLANNED are for this one job.

(Actually, may be better to give a variable instead of saying "1" job.)


The obvious equation.
Solve for t, and use it for the "planned" part of the description to find how many acres was the one job.
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Farmers mowed 60 acres of grass a day instead of 50 and managed to finish the task one day earlier than planned.
What is the area of the meadow they were mowing?
~~~~~~~~~~~~~~~~~~~ 

The direct translation the condition to math is this equation

 = 1,

where "x" is the area under the question.

 is the time required to complete the job mowing 50 acres per day.

 is the time required to complete the job mowing 60 acres per day.

1 on the right is the time difference, according to the condition.

Mulpiply both sides by LCD(50,60) = 300. You will get

6x - 5x = 300,

1x = 300  --->  x = 300.

Answer.  The area of the meadow they were mowing was 300 acres.


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