Rational equations algebra 2 word problem

Question

Hardy can wax his Triumph TR3 in 4 hours when working alone. If Ellie helps him, the job takes only 3 hours. How long would it take Ellie by herself?

Answer 1

Let x = number of hours that it takes Ellie to wax the car

 

1/4 = portion done by Hardy in 1 hour

1/x = portion done by Ellie in 1 hour

1/3 = portion done by both in 1 hour

 

1/4 + 1/x = 1/3

 

Multiply by the LCD, 12x:  3x + 12 = 4x

                                             x = 12 hours

 

If Ellie works alone, it would take her 12 hours to wax the car.