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- anonymous

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.

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- anonymous

HElp

- anonymous

don't even know where to start!!

- kropot72

In 1 hour Matthew, working alone, will wash 1/14 of the cars.
In 1 hour Arianna, working alone, will wash 1/11 of the cars.
Let the time taken to wash all of the cars working together be t hours.
Then we can write:
\[\large \frac{1}{14}+\frac{1}{11}=\frac{1}{t}\]
@lizzieeej Can you follow this reasoning?

- anonymous

Yes, but where from here?
@kropot72

- kropot72

Well, we have the required equation. Now we are asked to solve it to find the value of t.

- anonymous

so add 1/14 and 1/11 ? @kropot72

- kropot72

Yes, that is the first step.

- anonymous

you get 25/154

- anonymous

you can make it into decimal form if needed

- anonymous

so 6.16

- kropot72

Correct. So you now have
\[\large \frac{25}{154}=\frac{1}{t}\]

- anonymous

i made 25/154 equal 6.16 and then simplified to t=6.16

- kropot72

Yes, the time taken is 6.16 hours.

- anonymous

thanks so much!!!

- kropot72

You're welcome :)

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