1. 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

2. If one more than three times a number is divided by the number, the result is four thirds. Find the number. LCD = 3x Problem Solving 12.6 – Rational Expressions

3. 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? Time to sort one batch (hours) Fraction of the job completed in one hour Ryan Mike Together 2 3 x Problem Solving 12.6 – Rational Expressions

4. Time to sort one batch (hours) Fraction of the job completed in one hour Ryan Mike Together 2 3 x hrs. LCD =6x Problem Solving 12.6 – Rational Expressions

5. 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? Time to Assemble one unit (hours) Fraction of the job completed in one hour Mary Jim Together 2 8 x Problem Solving 12.6 – Rational Expressions

6. Time to Assemble one unit (hours) Fraction of the job completed in one hour Mary Jim Together 2 8 x LCD: hrs. 8x Problems about Numbers 12.6 – Rational Expressions

7. 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? Time to fill a tank (minutes) Fraction of the job completed in one minute 1 st pump 2 nd pump Together 3x x Problem Solving 12.6 – Rational Expressions 15

8. Problem Solving 12.6 – Rational Expressions Time to fill a tank (minutes) Fraction of the job completed in one minute 1 st pump 2 nd pump Together 3x x 15

9. LCD: min. 15x Problem Solving 12.6 – Rational Expressions min.

10. 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? Time to pump one basement (hours) Fraction of the job completed in one hour 1 st pump 2 nd pump Together x 12 Problem Solving 12.6 – Rational Expressions

11. Time to pump one basement (hours) Fraction of the job completed in one hour 1 st pump 2 nd pump Together x 12 Problem Solving 12.6 – Rational Expressions

12. LCD: hrs. 60x Problem Solving 12.6 – Rational Expressions

13. Problem Solving 12.6 – Rational Expressions 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 timed = r * t Rate upstream is 3 mph less than the rate downstream. d/t = r r upstream = 9 / t r downstream = 11 / t LCD = t