RATIONAL
WORD
PROBLEMS
TO SOLVE RATIONAL
WORD PROBLEMS
TO SOLVE RATIONAL
WORD PROBLEMS
1. Set up the unknowns in one variable.
TO SOLVE RATIONAL
WORD PROBLEMS
1. Set up the unknowns in one variable.
2. Set up an equation for the situation.
TO SOLVE RATIONAL
WORD PROBLEMS
1. Set up the unknowns in one variable.
2. Set up an equation for the situation.
3. Multiply by the common denominator
to clear out fractions.
TO SOLVE RATIONAL
WORD PROBLEMS
1. Set up the unknowns in one variable.
2. Set up an equation for the situation.
3. Multiply by the common denominator
to clear out fractions.
4. Solve the remaining equation for the
variable.
TO SOLVE RATIONAL
WORD PROBLEMS
1. Set up the unknowns in one variable.
2. Set up an equation for the situation.
3. Multiply by the common denominator
to clear out fractions.
4. Solve the remaining equation for the
variable.
5. State final answers in real world
terms.
Most tunnels are drilled using tunnel-boring
machines that begin at both ends of the tunnel.
Suppose a new underwater tunnel is being built
and one tunnel-boring machine alone can finish
the tunnel in 4 years. A different type of
machine can tunnel to the other side in 3 years.
If both machines start at opposite ends and
work at the same time, when will the tunnel be
finished?
Let x = number of years together
Let x = number of years together
Equation:
1 job
1 job
1 job


4 years 3 years x together
Let x = number of years together
Equation:
1 job
1 job
1 job


4 years 3 years x together
1
1
1


4
3
x
Solve equation: multiply by
common denominator (4)(3)(x).
Solve equation: multiply by
common denominator (4)(3)(x).
1(3 x )  1(4 x )  1(4)(3)
Solve equation: multiply by
common denominator (4)(3)(x).
1(3 x )  1(4 x )  1(4)(3)
3x  4x  12
Solve equation: multiply by
common denominator (4)(3)(x).
1(3 x )  1(4 x )  1(4)(3)
3x  4x  12
7 x  12
Solve equation: multiply by
common denominator (4)(3)(x).
1(3 x )  1(4 x )  1(4)(3)
3x  4x  12
7 x  12
12
x 
7
5
or 1
7
years
If both machines work toward
each other it will take 1.7
years to finish the tunnel.
If both machines work toward
each other it will take 1.7
years to finish the tunnel.
A car travels 300 km in the same time
that a freight train travels 200 km.
The speed of the car is 20 km/hr more
than the speed of the train. Find the
speed of the car and the speed of the
train.
A car travels 300 km in the same time
that a freight train travels 200 km.
The speed of the car is 20 km/hr more
than the speed of the train. Find the
speed of the car and the speed of the
train.
Let x = speed of train
Let x + 20 = speed of car
A car travels 300 km in the same time
that a freight train travels 200 km.
The speed of the car is 20 km/hr more
than the speed of the train. Find the
speed of the car and the speed of the
train.
Let x = speed of train
Let x + 20 = speed of car
Use the formula d = rt. Solve for “t”.
Use the formula d = rt. Solve for “t”.
t = d/r
Use the formula d = rt. Solve for “t”.
t = d/r
t car  t train
Use the formula d = rt. Solve for “t”.
t = d/r
t car  t train
dcar
dtrain

rcar
rtrain
Use the formula d = rt. Solve for “t”.
t = d/r
t car  t train
dcar
dtrain

rcar
rtrain
300
200

x  20
x
Solve: multiply by the common
denominator (x + 20)(x).
Solve: multiply by the common
denominator (x + 20)(x).
300 x  200( x  20)
Solve: multiply by the common
denominator (x + 20)(x).
300 x  200( x  20)
300x  200x  4000
Solve: multiply by the common
denominator (x + 20)(x).
300 x  200( x  20)
300x  200x  4000
100x  4000
Solve: multiply by the common
denominator (x + 20)(x).
300 x  200( x  20)
300x  200x  4000
100x  4000
x  40
Speed of train = x = 40 km/hr
Speed of train = x = 40 km/hr
Speed of car = x + 20 = 60 km/hr
Speed of train = x = 40 km/hr
Speed of car = x + 20 = 60 km/hr
One electronic reader can read a deck
of punched cards in half the time of
another reader. Together they can
read the deck in 8 minutes. How long
would it take each reader alone to
read the deck?
One electronic reader can read a deck
of punched cards in half the time of
another reader. Together they can
read the deck in 8 minutes. How long
would it take each reader alone to
read the deck?
Let x = first reader time
One electronic reader can read a deck
of punched cards in half the time of
another reader. Together they can
read the deck in 8 minutes. How long
would it take each reader alone to
read the deck?
Let x = first reader time
Let 2x = second reader time
One electronic reader can read a deck
of punched cards in half the time of
another reader. Together they can
read the deck in 8 minutes. How long
would it take each reader alone to
read the deck?
Let x = first reader time
Let 2x = second reader time
1
1
1


x
2x
8
Solve: multiply by common
denominator (x)(8)
Solve: multiply by common
denominator (x)(8)
1(8)  1(4)  1( x )
Solve: multiply by common
denominator (x)(8)
1(8)  1(4)  1( x )
12  x
Solve: multiply by common
denominator (x)(8)
1(8)  1(4)  1( x )
12  x
First reader = x = 12 minutes
Second reader = 2x = 24 minutes
One pipe can fill a tank in 6 hours
while another can empty it in 2 hours.
How long will it take to empty the full
tank if both pipes are open at once?
One pipe can fill a tank in 6 hours
while another can empty it in 2 hours.
How long will it take to empty the full
tank if both pipes are open at once?
Let x = time to empty full tank
One pipe can fill a tank in 6 hours
while another can empty it in 2 hours.
How long will it take to empty the full
tank if both pipes are open at once?
Let x = time to empty full tank
Part empty - Part fill = Total empty
One pipe can fill a tank in 6 hours
while another can empty it in 2 hours.
How long will it take to empty the full
tank if both pipes are open at once?
Let x = time to empty full tank
Part empty - Part fill = Total empty
1 1
1


2 6
x
Solve: multiply by the common
denominator (x)(6).
Solve: multiply by the common
denominator (x)(6).
1( x )(3)  1( x )  1(6)
Solve: multiply by the common
denominator (x)(6).
1( x )(3)  1( x )  1(6)
2x  6
Solve: multiply by the common
denominator (x)(6).
1( x )(3)  1( x )  1(6)
2x  6
x 3
Solve: multiply by the common
denominator (x)(6).
1( x )(3)  1( x )  1(6)
2x  6
x 3
It will take 3 hours to empty the tank.
TO SOLVE RATIONAL
WORD PROBLEMS
1. Set up variables.
2. Set up equation.
3. Multiply by the common
denominator.
4. Solve for variables.
5. Define final answers.
PRACTICE
TIME
GO FOR
IT!!!!