Question

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.

Answer 1

• ≈ 6 hours 10 minutes

Explanation:

• Matthew can wash all the cars in 14 hours ⇒ 1/14 of all cars in 1 hour
• Arianna can wash all the cars in 11 hours ⇒ 1/11 of all cars in 1 hour

Together they can wash in 1 hour:

• 1/14 + 1/11 = 25/154

Time needed to wash all the cars:

• 154/25 = 6.16 hours ≈ 6 hours 10 minutes