It takes Roberto eight hours longer than Paula to repair a transmission. If it takes three hours to do the job if they work together, how long will it take each of them working alone?

Paula = 4 hours

Roberto = 12 hours

Step-by-step explanation:

Time taken by Paula = x

Time taken by Roberto = x +. 8

Paula's rate = 1/x

Roberto's rate = 1/(x + 8)

Combined rate = 1/3

Time it takes each if them working alone ;

Paula's rate + Roberto's rate = combined rate

1 /x + 1 / (x +8) = 1/3

Take the L. C. M

((x+8) + x) / x(x+8) = 1/3

(2x + 8) / x(x + 8) = 1/3

3(2x + 8) = x(x + 8)

6x + 24 = x² + 8x

x² + 8x - 6x - 24 = 0

x² + 2x - 24 = 0

Solving the quadratic equation :

x² + 6x - 4x - 24 = 0

x(x + 6) - 4(x + 6) = 0

(x - 4) = 0 or (x + 6) = 0

x = 4 or x = - 6

Time taken cannot be negative

Hence, x = 4

Hence, working alone, it takes ;

Time taken by Paula = 4

Time taken by Roberto = 4 + 8 = 12

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