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?
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.
@whpalmer4 how do you combine the rates?
Do you know how to add fractions?
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.
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.
thank you @whpalmer4
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