Download Assignment: Solve Rational Equations

Assignment: Solve Rational Equations
Follow the directions to solve each problem. Show all work leading to your answer.
1. Shaun and Kendra want to scan old family photos into a computer photo organizing
program. On his laptop Shaun can scan about five photos in three minutes. Kendra can
scan about eight photos in five minutes on her computer. Working together, how many
minutes (t) would it take for both of them to scan 36 photos?
a. Fill in the blanks in the table below to find the ratios to represent the various photo
scanning rates. Then use the ratios to write a rational equation.
Shaun’s
Scanning Rate
___ photos
___ minutes
+
+
Kendra’s
Scanning Rate
___ photos
___ minutes
=
=
Combined
Scanning Rate
___ photos
___ minutes
Equation: _______________________
{5 photos / 3 minutes} + {8 photos / 5 minutes} = {36 photos / "t" minutes}
b. Identify the LCD for the equation. Solve the equation by multiplying both sides by the
LCD. Show all the steps necessary to find the answer. Then write a sentence to
describe what the answer means for this situation.
LCD: 15t
[ 15t(5/3) ] + [ 15t(8/5) ] = [ 15t(36/t) ]
25t + 24t = 540
49t = 540
t = 11 and 1/49
Shaun and
Kendra
both
together,
a little moreswimming
then 11 minutes
scan
2. If
Ricardo
plans
to use
twowork
garden
hosesittowould
fill antake
above-ground
pool intohis
36
photos.
backyard. By itself, the first hose could fill the pool in 12 hours. The second hose could fill
the pool in 10 hours. About how many hours (t) would it take if Ricardo uses both hoses
to fill the pool?
a. Fill in the blanks in the table below to find the ratios to represent the various pool
filling rates. Then use the ratios to write a rational equation.
First Garden
Hose
Fill Rate
___ pool
___ hours
+
+
Second Garden
Hose
Fill Rate
___ pool
___ hours
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=
=
Combined
Fill Rate
___ pool
___ hours
Equation: _______________________
{1 pool / 12 hours} + {1 pool / 10 hours} = {1 pool / "t" hours}
b. Identify the LCD for the equation. Solve the equation by multiplying both sides by the
LCD. Show all the steps necessary to find the answer. Then write a sentence to
describe what the answer means for this situation.
LCD: 60t
[60t(1/12)] + [60t(1/10)] = [60t(1/t)]
5t + 6t = 60
11t = 60
t = 5 and 5/11
If Ricardo uses
bothahoses
pool, ittowould
fivethe
hours
to fill. can grade
3. Professor
Ma has
stacktooffill40the
essays
grade.take
By about
herself,
professor
about five essays in two hours. Her teaching assistant, Chen, can grade about seven
essays in three hours. About how many hours (t) would it take both of them to grade all
40 essays if they work together?
a. Fill in the blanks in the table below to find the ratios to represent the various essay
grading rates. Then use the ratios to write a rational equation.
Professor Ma’s
Grading Rate
___ essays
___ hours
+
+
Chen’s Grading
Rate
___ essays
___ hours
=
=
Combined
Grading Rate
___ essays
___ hours
Equation: _______________________
{5 essays / 2 hours} + {7 essays / 3 hours} = {40 essays / "t" hours}
b. Identify the LCD for the equation. Solve the equation by multiplying both sides by the
LCD. Show all the steps necessary to find the answer. Then write a sentence to
describe what the answer means for this situation.
LCD: 6t
[6t(5/2)] + [6t(7/3)] = [6t(40/t)]
15t + 14t = 240
29t = 240
t = 8 and 8/29
4. Next,
your Ma
ownand
problem
that can
be solved
with
rational
equation.
of a 8
If bothwrite
Professor
Chen work
together
to grade
40aessays,
it would
takeThink
them about
situation
hours. where two people (or things) can work together to finish a job in less time than it
takes each of them to work alone.
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a. Write 3-4 sentences to describe the situation. Then ask a question that can be
solved using a rational equation. Be sure to include enough information so that
someone reading the problem can write an equation to solve the problem.
Mary and Maya want to paint a room. Working alone, Mary can finish the job in 6 hours. If
Maya works alone, she can finish it in 8 hours. If they both work together, how many hours
would it take to paint the room?
b. Define the variable in the problem and create a table to organize the information
described in your problem. Then use the contents of the table to write a rational
equation.
Variable:______________
Rate #1
+
Rate #2
=
Combined
Rate
Equation: _______________________
t = number of hours it both work together
{1 room / 6 hours} + {1 room / 8 hours} = {1 / "t"}
c.
Identify the LCD for the equation. Solve the equation by multiplying both sides by
the LCD. Show all the steps necessary to find the answer. Then write a sentence
to describe what the answer means for this situation.
LCD: 24t
[24t(1/6)] + [24t(1/8)] = [24t(1/t)]
4t + 3t = 24
7t = 24
t = 3 and 3/7
If both Mary and Maya worked together to paint the room, it would take them about 3
hours.
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