New SAT Math Workbook

Powell to do the job alone solution if it takes mr

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Unformatted text preview: e route. One car averages 36 miles per hour and the other 31 miles per hour. In how many hours will the faster car be 30 miles ahead of the slower car? (A) 3 (B) (C) (D) (E) 3 4 6 6 1 4 1 2 5. 2. 3. www.petersons.com Problem Solving in Algebra 185 8. WORK PROBLEMS In most work problems, a job is broken up into several parts, each representing a fractional portion of the entire job. For each part represented, the numerator should represent the time actually spent working, while the denominator should represent the total time needed to do the job alone. The sum of all the individual fractions must be 1 if the job is completed. Example: John can complete a paper route in 20 minutes. Steve can complete the same route in 30 minutes. How long will it take them to complete the route if they work together? Solution: John Time actually spent Time needed to do entire job alone x 20 Steve x 30 + = 1 Multiply by 60 to clear fractions. 3x + 2 x = 60 5 x = 60 x = 12 Example: Mr. Powell can mow his lawn twice as fast as his son Mike. Together they do the job in 20 minutes. How many minutes would it take Mr. Powell to do the job alone? Solution: If it takes Mr. Powell x hours to mow the lawn, Mike will take twice as long, or 2x hours, to mow the lawn. Mr. Powell Mike 20 x + 20 2x = 1 Multiply by 2x to clear fractions. 40 + 20 = 2 x 60 = 2 x x = 30 minutes www.petersons.com 186 Chapter 12 Exercise 8 Work out each problem. Circle the letter that appears before your answer. 1. Mr. White can paint his barn in 5 days. What part of the barn is still unpainted after he has worked for x days? (A) (B) (C) (D) (E) 2. x 5 5 x x−5 x 5− x x 5− x 5 4. Mr. Jones can plow his field with his tractor in 4 hours. If he uses his manual plow, it takes three times as long to plow the same field. After working with the tractor for two hours, he ran out of gas and had to finish with the manual plow. How long did it take to complete the job after the tractor ran out of gas? (A) 4 hours (B) 6 hours (C) 7 hours (D) 8 hours (E) 8 1 hours 2 Mary can clean the hous...
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