Jordan is a manager of a car dealership. He has two professional car washers, Matthew and Arianna, to clean the entire lot of cars. Matthew can wash all the cars in 14 hours. Arianna can wash all the cars in 11 hours. Jordan wants to know how long it will take them to wash all the cars in the lot if they work together. Write an equation and solve for the time it will take Matthew and Arianna to wash all the cars together. Explain each step.

6.16 hours

Step-by-step explanation:

Let the number of hours that washed the car together = T

Number of hours Matthew washed = m = 14 hours

Number of hours Arianna washed = a = 11 hours

The formula to calculate how many they wash the cars together is given as

1/a + 1/m = 1/T

1/14 + 1/11 = 1/T

Lowest Common Denominator = 154

Hence:

(11 + 14)/154 = 1/T

25/154 = 1/T

Cross Multiply

154 × 1 = 25 × T

T = 154/25

T = 6.16 hours

Therefore, it will take Matthew and Arianna 6.16 hours to wash the cars together

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