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RATIONAL WORD PROBLEMS
RATIONAL
WORDPROBLEMS
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.
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.
TO SOLVE RATIONAL WORD PROBLEMS
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 togetherEquation:1 job 1 job 1 job
4 years 3 years together
x
Let x = number of years togetherEquation:1 job 1 job 1 job
4 years 3 years x together
1 1 14 3 x
Solve equation: multiply by common denominator (4)(3)(x).
Solve equation: multiply by common denominator (4)(3)(x).
1(3 ) 1(4 ) 1(4)(3)x x
Solve equation: multiply by common denominator (4)(3)(x).
1(3 ) 1(4 ) 1(4)(3)x x
3 4 12x x
Solve equation: multiply by common denominator (4)(3)(x).
7 12x
1(3 ) 1(4 ) 1(4)(3)x x
3 4 12x x
Solve equation: multiply by common denominator (4)(3)(x).
12 5 or 1 years7 7
x
7 12x
1(3 ) 1(4 ) 1(4)(3)x x
3 4 12x x
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/h 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/h more than the speed of the train. Find the speed of the car and the speed of the train.
Let x = speed of trainLet 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/h more than the speed of the train. Find the speed of the car and the speed of the train.
Let x = speed of trainLet x + 20 = speed of car
Use the formula d = rt. Solve for “t”.
t = d/rUse the formula d = rt. Solve for “t”.
t = d/r
car traint t
Use the formula d = rt. Solve for “t”.
t = d/r
car traint t
car train
car train
d dr r
Use the formula d = rt. Solve for “t”.
t = d/r
car traint t
car train
car train
d dr r
300 20020
x x
Use the formula d = rt. Solve for “t”.
Solve: multiply by the common denominator (x + 20)(x).
Solve: multiply by the common denominator (x + 20)(x).
300 200( 20)x x
Solve: multiply by the common denominator (x + 20)(x).
300 200 4000x x
300 200( 20)x x
Solve: multiply by the common denominator (x + 20)(x).
300 200 4000x x
100 4000x
300 200( 20)x x
Solve: multiply by the common denominator (x + 20)(x).
300 200 4000x x
100 4000x
40x
300 200( 20)x x
Speed of train = x = 40 km/h
Speed of train = x = 40 km/hSpeed of car = x + 20 = 60 km/h
Speed of train = x = 40 km/hSpeed of car = x + 20 = 60 km/h
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 timeLet 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?
1 1 12 8x x
Let x = first reader timeLet 2x = second reader time
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)
12 x1(8) 1(4) 1( )x
Solve: multiply by common denominator (x)(8)
First reader = x = 12 minutesSecond reader = 2x = 24 minutes
1(8) 1(4) 1( )x 12 x
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?
Part empty - Part fill = Total empty
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?
1 1 12 6 x
Part empty - Part fill = Total empty
Let x = time to empty full tank
Solve: multiply by the common denominator (x)(6).
Solve: multiply by the common denominator (x)(6).
1( )(3) 1( ) 1(6)x x
Solve: multiply by the common denominator (x)(6).
2 6x 1( )(3) 1( ) 1(6)x x
Solve: multiply by the common denominator (x)(6).
2 6x 3x
1( )(3) 1( ) 1(6)x x
Solve: multiply by the common denominator (x)(6).
2 6x 3x
It will take 3 hours to empty the tank.
1( )(3) 1( ) 1(6)x x
1. Set up variables.2. Set up equation.3. Multiply by the common denominator.4. Solve for variables.5. Define final answers.
TO SOLVE RATIONAL WORD PROBLEMS
PRACTICETIME
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