Question

Two​ mechanics, Bonita Rich, ​and Pamela​ Pearso​n, 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?

Answer 1

• Bonita: 12.66 hours
• Pamela: 15.66 hours

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.