anonymous
  • 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.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
anonymous
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anonymous
  • anonymous

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anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous
HElp
anonymous
  • anonymous
don't even know where to start!!
kropot72
  • 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
  • anonymous
Yes, but where from here? @kropot72
kropot72
  • kropot72
Well, we have the required equation. Now we are asked to solve it to find the value of t.
anonymous
  • anonymous
so add 1/14 and 1/11 ? @kropot72
kropot72
  • kropot72
Yes, that is the first step.
anonymous
  • anonymous
you get 25/154
anonymous
  • anonymous
you can make it into decimal form if needed
anonymous
  • anonymous
so 6.16
kropot72
  • kropot72
Correct. So you now have \[\large \frac{25}{154}=\frac{1}{t}\]
anonymous
  • anonymous
i made 25/154 equal 6.16 and then simplified to t=6.16
kropot72
  • kropot72
Yes, the time taken is 6.16 hours.
anonymous
  • anonymous
thanks so much!!!
kropot72
  • kropot72
You're welcome :)

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