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Problem Solving

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12.6 – Rational Expressions

Problem Solving

The quotient of a number and 2 minus 1/3 is the quotient of a number and 6. Find the number.

LCD = 6

12.6 – Rational Expressions

Problem Solving

If one more than three times a number is divided by the number, the result is four thirds. Find the number.

LCD = 3x

12.6 – Rational Expressions

Time to sort one batch (hours)

Fraction of the job completed in one hour

Ryan

Mike

Together

Problem Solving

Mike and Ryan work at a recycling plant. Ryan can sort a batch of recyclables in 2 hours and Mike can short a batch in 3 hours. If they work together, how fast can they sort one batch?

2

3

x

12.6 – Rational Expressions

Time to sort one batch (hours)

Fraction of the job completed in one hour

Ryan

Mike

Together

Problem Solving

2

3

x

LCD =

6x

hrs.

12.6 – Rational Expressions

Time to Assemble one unit (hours)

Fraction of the job completed in one hour

Mary

Jim

Together

Problem Solving

Jim and Mary assemble Iron Man action figures. It takes Mary 2 hours to assemble one figure while it takes Jim 8 hours. How long will it take them to assemble one figure if they work together?

2

8

x

12.6 – Rational Expressions

Time to Assemble one unit (hours)

Fraction of the job completed in one hour

Mary

Jim

Together

Problems about Numbers

2

8

x

LCD:

8x

hrs.

12.6 – Rational Expressions

Time to fill a tank (minutes)

Fraction of the job completed in one minute

1st pump

2nd pump

Together

Problem Solving

A pump can fill a tank three times as fast as another pump. If the pumps work together, they could fill the tank in fifteen minutes. How long would it take each pump to fill the tank alone?

x

3x

15

12.6 – Rational Expressions

Time to fill a tank (minutes)

Fraction of the job completed in one minute

1st pump

2nd pump

Together

Problem Solving

x

3x

15

12.6 – Rational Expressions

Problem Solving

15x

LCD:

min.

min.

12.6 – Rational Expressions

Time to pump one basement (hours)

Fraction of the job completed in one hour

1st pump

2nd pump

Together

Problem Solving

A sump pump can pump water out of a basement in twelve hours. If a second pump is added, the job would only take six and two-thirds hours. How long would it take the second pump to do the job alone?

12

x

12.6 – Rational Expressions

Time to pump one basement (hours)

Fraction of the job completed in one hour

1st pump

2nd pump

Together

Problem Solving

12

x

12.6 – Rational Expressions

Problem Solving

LCD:

60x

hrs.

12.6 – Rational Expressions

Problem Solving

A boat can travel 9 miles upstream in the same amount of time it takes to travel 11 downstream. If the current of the river is 3 miles per hour, find the speed of the boat going upstream and downstream.

distance = rate x time

d = r * t

d/t = r

Rate upstream is 3 mph less than the rate downstream.

rupstream = 9/t

rdownstream = 11/t

LCD = t