Solving Word Problems With Equations Of One Degree And One Unknown Worksheet With Answers Page 13
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2060 + 2X = 3X
60 = X
It takes you 60 days to build the house alone.
EXAMPLE
1. One pipe can fill a tank in 18 minutes and another pipe can fill it in 24 minutes. The
drainpipe can empty the tank in 15 minutes. An inefficient worker leaves the
drainpipe open. With all pipes open, how long will it take to fill the tank?
Solution:
Let X = time it takes to fill the tank. Each pipe will “work” that length of
!
time.
!
The first pipe has rate 1/18 of the tank per minute
!
The second pipe has rate 1/24 of the tank per minute
!
The drainpipe has rate -1/15 of the tank per minute. Since the drainpipe is
!
undoing the job, it is given a negative rate.
Rate
Time
Amount of Work
Pipe 1
1/8
X
(1/18) X
Pipe 2
1/24
X
(1/24) X
Drain
-1/15
X
(-1/15) X
Since the problem does not address the idea of combined rate, we do not have a
!
combined” row in the chart.
These three pipes are going to do the whole job of filling the tank.
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Work of pipe 1 + work of pipe 2 - work of drain = whole or 100%
!
1
1
1
−
x
+
x
x
=
1
18
24
15
You can do the rest of this problem.
!
Answer: 32 8/11 hr.
!
PRACTICE PROBLEMS
NUMBER PROBLEMS
1. Four times a number decreased by 12 is three times the number. Find the number.
Let x=number
4x-12=3x
4x-3x=12
x=12
2. A certain number decreased by 5 is twice the number. Find it.
Let x=number
x-5=2x
x-2x=+5
13
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