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Mathematics 37 Online
OpenStudy (anonymous):

Two car washers, Michelle and Nancy, are working on your car. Michelle can complete the work in 6 hours, while Nancy can complete the work in 3 hours. How many hours does the car washing take if they work together?

OpenStudy (whpalmer4):

Michelle does 1 car in 6 hours, so her hourly rate is 1/6 car/hour, right? Nancy similarly does 1 car in 3 hours, so her hourly rate is 1/3 car/hour. Add the two rates together and use that combined rate to find the time for both to wash the car working together.

OpenStudy (anonymous):

@whpalmer4 how do you combine the rates?

OpenStudy (whpalmer4):

Do you know how to add fractions?

OpenStudy (whpalmer4):

What does \[\frac{1}{6}+\frac{1}3 = \]That is the combined rate, or fraction of a car the two of them can wash in an hour, working together.

OpenStudy (whpalmer4):

If you think about it, if Michelle starts at one end, and Nancy starts at the other end, after 1 hour, Michelle will have washed 1/6 of the car, and Nancy will have washed 1/3 of the car. Together, they will have washed \(\dfrac{1}6+\dfrac{1}3\) of the car. After another hour, they will have washed a total of \[\frac{1}{6}+\frac{1}{6}+\frac{1}3+\frac{1}{3}\] of the car.

OpenStudy (anonymous):

thank you @whpalmer4

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