Solving Word Problems With Equations Of One Degree And One Unknown Worksheet With Answers Page 12
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20!
Rate of Work
Time
Amount of Work
First Person
Second Person
Combined
Go back and reread the problem.
!
You are asked to find how long it would take you to build the house alone
!
Call that time “X”. If you can build a house in “X” hours, your rate would be
!
1/X.
The man’s rate is 1/30. Since he can build the house in 30 days, his rate is 1/30
!
per day.
The “combined” rate is 1/20.
!
To build it together in 20 days means your combined rate is 1/20 of the job per
!
day
For this particular problem the completed chart would look like.
!
Rate of Work
Time
Amount of Work
First Person
1/X
Y
(1/X)Y
Second Person
1/30
Y
(1/30)Y
Combined
1/20
Y
(1/20) Y
What this amounts to is ignoring time when the time of each person or machine is
!
the same AND when there already is another unknown.
Solve fractional equations by multiplying each term by the least common
!
denominator of all the fractions. (Here that is 60x). This gets rid of fractions.
60 +
2X
=
3X
60 =
X
The problem asked “how long would it take you to build the house;” this you
!
represented by X. Therefore it would take you 60 days to build it alone.
A “write-up” of the problem is shown below. We need a statement about X at the
!
beginning of this problem write-up since x, by itself, is not in the chart.
Let X = the number of days it takes you to build the house alone.
!
--------------------WORK-------------------------------------
Rate
Time
Amount
You
1/X
Y
(1/X) * Y
Man
1/30
Y
(1/30X) * Y
Combined
1/20
Y
(1/20X) * Y
1
1
1
y
+
y
=
y
x
30
20
1
1
1
+
=
x
30
20
12
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