RATIONAL

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RATIONAL

WORDPROBLEMS

TO SOLVE RATIONAL WORD PROBLEMS

1. Set up the unknowns in one variable.

1. Set up the unknowns in one variable.2. Set up an equation for the situation.

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.

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 togetherEquation:1 job 1 job 1 job

4 years 3 years x together

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).

1(3 ) 1(4 ) 1(4)(3)x x

3 4 12x x

1(3 ) 1(4 ) 1(4)(3)x x

3 4 12x x

12 5 or 1 years7 7

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.

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 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/hr 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

t = d/r

car traint t

car train

d dr r

t = d/r

car traint t

car train

d dr r

300 200x 20 x

Solve: multiply by the common denominator (x + 20)(x).

300 200( 20)x x

300 200 4000x x

300 200( 20)x x

300 200 4000x x

100 4000x

300 200( 20)x x

300 200 4000x x

100 4000x

300 200( 20)x x

Speed of train = x = 40 km/hr

Speed of train = x = 40 km/hrSpeed 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 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)

1(8) 1(4) 1( )x

12 x1(8) 1(4) 1( )x

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

Part empty - Part fill = Total empty

Let x = time to empty full tank

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).

1( )(3) 1( ) 1(6)x x

2 6x 1( )(3) 1( ) 1(6)x x

2 6x 3x

1( )(3) 1( ) 1(6)x x

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.

PRACTICETIME

GO FOR IT!!!!

RATIONAL

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