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

@surryyy @mathmath333 @help_people

Answer 2

@zepdrix

Answer 3

@acxbox22

Answer 4

@zepdrix

Answer 5

@dan815

Answer 6

HElp

Answer 7

don't even know where to start!!

Answer 8

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?

Answer 9

Yes, but where from here?
@kropot72

Answer 10

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

Answer 11

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

Answer 12

Yes, that is the first step.

Answer 13

you get 25/154

Answer 14

you can make it into decimal form if needed

Answer 15

so 6.16

Answer 16

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

Answer 17

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

Answer 18

Yes, the time taken is 6.16 hours.

Answer 19

thanks so much!!!

Answer 20

You're welcome :)