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Problems about Numbers If one more than three times a number is divided by the number, the result is four thirds. Find the number. LCD = 3x 5.6 – Applications

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Problems about Work Mike and Ryan work at a recycling plant. Ryan can sort a batch of recyclables in 2 hours and Mike can sort 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 5.6 – Applications

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Problems about Work Time to sort one batch (hours) Fraction of the job completed in one hour Ryan Mike Together 2 3 x hrs. LCD =6x 5.6 – Applications

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James and Andy mow lawns. It takes James 2 hours to mow an acre while it takes Andy 8 hours. How long will it take them to mow one acre if they work together? Time to mow one acre (hours) Fraction of the job completed in one hour James Andy Together 2 8 x 5.6 – Applications

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Time to mow one acre (hours) Fraction of the job completed in one hour James Andy Together 2 8 x LCD: hrs. 8x 5.6 – Applications

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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 5.6 – Applications

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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 5.6 – Applications

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LCD: hrs. 60x 5.6 – Applications

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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? 5.6 – Applications

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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 5.6 – Applications

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RateTimeDistance Motor- cycle Car x x + 15 450 mi 600 mi t t LCD:x(x + 15) 5.6 – Applications

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x(x + 15) Motorcycle Car 5.6 – Applications

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RateTimeDistance Up Stream Down Stream 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 x - 5 x + 5 22 mi 42 mi t t 5.6 – Applications

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RateTimeDistance Up Stream Down Stream boat speed = x x - 5 x + 5 22 mi 42 mi t t LCD:(x – 5)(x + 5) 5.6 – Applications

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Boat Speed (x – 5)(x + 5) 5.6 – Applications

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Review of Long Division 5.7 – Division of Polynomials

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Long Division 5.7 – Division of Polynomials

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Long Division 5.7 – Division of Polynomials

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Long Division 5.7 – Division of Polynomials

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Real World Problems MA.912.A.5.7 Solve real-world problems involving rational equations (mixture, distance, work, interest, and ratio).

Real World Problems MA.912.A.5.7 Solve real-world problems involving rational equations (mixture, distance, work, interest, and ratio).

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