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Problem Solving

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.

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Problem Solving

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  1. 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

  2. 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

  3. 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

  4. 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.

  5. 12.6 – Rational Expressions Time to Assemble one unit (hours) Fraction of the job completed in one hour Merry Pippen Together Problem Solving Pippen and Merry assemble Ork action figures. It takes Merry 2 hours to assemble one figure while it takes Pippen 8 hours. How long will it take them to assemble one figure if they work together? 2 8 x

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

  7. 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

  8. 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

  9. 12.6 – Rational Expressions Problem Solving LCD: 60x hrs.

  10. 12.6 – Rational Expressions Problem Solving Distance, Rate and Time Problems If you drive at a constant speed of 65 miles per hour and you travel for 2 hours, how far did you drive?

  11. 12.6 – Rational Expressions Problem Solving A car travels six hundred miles in the same time a motorcycle travels four hundred and fifty miles. If the car’s speed is fifteen miles per hour faster than the motorcycle’s, find the speed of both vehicles. x t 450 mi t x + 15 600 mi

  12. 12.6 – Rational Expressions – Problem Solving x t 450 mi t x + 15 600 mi LCD: x(x + 15) x(x + 15) x(x + 15)

  13. 12.6 – Rational Expressions – Problem Solving x(x + 15) x(x + 15) Motorcycle Car

  14. 12.6 – Rational Expressions – Problem Solving A boat can travel twenty-two miles upstream in the same amount of time it can travel forty-two miles downstream. The speed of the current is five miles per hour. What is the speed of the boat in still water? boat speed x t x - 5 22 mi t x + 5 42 mi

  15. 12.6 – Rational Expressions – Problem Solving boat speed x t x - 5 22 mi t x + 5 42 mi LCD: (x – 5)(x + 5) (x – 5)(x + 5) (x – 5)(x + 5)

  16. 12.6 – Rational Expressions – Problem Solving (x – 5)(x + 5) (x – 5)(x + 5) Boat Speed

  17. 12.7 – Rational Expressions Simplifying Complex Fractions LCD: 63 Outersover Inners

  18. 12.7 – Rational Expressions Simplifying Complex Fractions LCD: 12, 8 LCD: 24

  19. 12.7 – Rational Expressions Simplifying Complex Fractions LCD: y y–y

  20. 12.7 – Rational Expressions Simplifying Complex Fractions LCD: 6xy 6xy 6xy

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