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Problems Involving Work

Rate of Work. Time. Amount Completed. Juan. 1/12. t. t /12. Rebecca. 1/8. t. t /8. Problems Involving Work.

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Problems Involving Work

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  1. Rate of Work Time Amount Completed Juan 1/12 t t/12 Rebecca 1/8 t t/8 Problems Involving Work • Example: Juan and Rebecca work during the summer painting houses. Juan can paint an average size house in 12 days, while Rebecca requires 8 days to do the same job. How long would it take them, working together, to paint an average size house? • 1.Introduction. A correct approach is to consider how much of the painting job is finished in one day. It takes Juan 12 days to finish painting a house, so his rate is 1/12 of the job per day. It takes Rebecca 8 days to do the painting alone, so her rate is 1/8 of the job per day. Let t = The time it takes both to complete the job together.

  2. Portion of work done by Rebecca in t days Portion of work done by Juan in t days continued • 2.Body. The time that we want is some number t for which 3.Conclusion. Together, it will take Juan and Rebecca 4 4/5 days to complete painting a house.

  3. Modeling Work Problems • If • a = the time needed for A to complete the work alone, • b = the time needed for B to complete the work alone, and • t = the time needed for A and B to complete the work together, • then • The following are equivalent equations that can also be used:

  4. x + 20 x Problems Involving Motion Example: Because of a tail wind, a jet is able to fly 20 mph faster than another jet that is flying into the wind. In the same time that it takes the first jet to travel 90 miles the second jet travels 80 miles. How fast is each jet traveling? 1.Introduction. Let x = speed of slower jet (mph) x + 20 = speed of faster jet (mph)

  5. Distance = Rate  Time • Fill in the blank column in the table. 2. Body Since the times must be the same for both planes, we have the equation Cross Multiply 3. Conclusion. One jet is traveling at 160 mph and the second jet is traveling at 180 mph.

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