Two mechanics, bonita rich, and pamela pearson, take 7 hours to rebuild an engine when they work together. if each worked alone, bonita, the more experienced mechanic, could complete the job 3 hours faster than pamela. how long would it take each of them to rebuild the engine working alone?

Step-by-step explanation:

Let b represent the number of hours it takes Bonita to rebuild an engine. Then b+3 is the number of hours it takes Pamela. When they work together, their total rate of work in "rebuilds per hour" is ...

  1/b + 1/(b+3) = 1/7

Multiplying by the product of the denominators, we have ...

  7(b+3) +7b = b(b+3)

  b² -11b = 21 . . . . . . . . . subtract 14b

  b² -11b +30.25 = 51.25 . . . . complete the square by adding (11/2)^2

  (b -5.5)² = 51.25 . . . . . . . . . . write as a square

  b = 5.5 + √51.25 . . . . . take the square root and add 5.5

  b ≈ 12.65891 . . . . hours

Working alone, Bonita could rebuild an engine in about 12.66 hours; Pamela could do it in about 15.66 hours.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

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−

4

x

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2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2