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Time and Rate Problems with Machines

Solve multiple-choice test grading time, pump filling tank time, and emblem production time problems using polynomials with rational coefficients. Understand working rates of different machines and find the time taken for them to complete tasks together.

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Time and Rate Problems with Machines

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  1. 6.10 Using Polynomials with Rational Coefficients

  2. 1. A scantron machine can grade a batch of multiple choice tests in 15 minutes. A newer model will do the same job in 12 minutes. How many minutes would it take both machine to complete the job working together? • What is the rate of the first machine? (how much of the job gets done per minute?) • What is the rate of the second machine? • If 1 is the total work done together in x minutes, write an equation to represent both machines working together.

  3. 2. One pump can fill a Kool-Aid tank in 30 minutes. Another pump can fill the tank in 45 minutes. How long would it take both pumps working together to fill the tank?

  4. 3. A stamping machine can produce the Ferrari emblem for the hood of the car every 18 seconds. A newer machine can produce the same part in 12 seconds. How long would it take the two machines to produce 50 emblems if working simultaneously?

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