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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

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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

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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

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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

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

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

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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

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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

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

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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? Problem Solving 12.6 – Rational Expressions

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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. RateTimeDistance Motor- cycle Car x x + 15 450 mi 600 mi t t Problem Solving 12.6 – Rational Expressions

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RateTimeDistance Motor- cycle Car x x + 15 450 mi 600 mi t t LCD:x(x + 15) 12.6 – Rational Expressions – Problem Solving

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

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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 RateTimeDistance Up Stream Down Stream x - 5 x + 5 22 mi 42 mi t t 12.6 – Rational Expressions – Problem Solving

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boat speed x RateTimeDistance Up Stream Down Stream x - 5 x + 5 22 mi 42 mi t t LCD:(x – 5)(x + 5) 12.6 – Rational Expressions – Problem Solving

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

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12.7 – Rational Expressions Simplifying Complex Fractions LCD:63 Outers over Inners

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

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LCD: y y–yy–y 12.7 – Rational Expressions Simplifying Complex Fractions

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

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You can use weighted averages to solve uniform motion problems when the objects you are considering are moving at constant rates or speeds.

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