Question

Jordan is a manager of a car dealership. He has 3 professional car washers to clean the entire lot of cars, Jennifer, Arianna, and Matthew. Jennifer can wash all the cars in 14 hours. Arianna can wash all the cars in 11 hours. Matthew is new to the car dealership, so no one knows how long it will take him. Hayden assigns all of them to wash the cars together. Explain to Jordan how this task can tell her how long it would take Matthew to complete the task if he worked by himself. Use complete sentences.

Answer 1

I need someone to help me with this I do not understand how this is adequate enough information to answer the question. I have to submit this by midnight Easter time

Answer 2

@ranga @cwrw238

Answer 3

@jim_thompson5910

Answer 4

Calculate the unit rate for each.

Jennifer can wash all the cars in 14 hours. Jennifer's work speed is 1/14 of the job per hour.

Arianna can wash all the cars in 11 hours. Arianna's work speed is 1/11 of the job per hour.

You'll have to time them to see how long it takes to complete the entire task.

Answer 5

Would that be the answer or do I need to make an equation of that and solve it?

Answer 6

@tkhunny

Answer 7

How would you solve this sort of problem?

Steve can paint the house in 12 hours.
Ralph can paint the house in 10 hours.
How long does it take them both, working together?

Answer 8

It would take them 22 hours.

Answer 9

@tkhunny

Answer 10

Very bad. Why would it take longer if they worked together? Try again.

Answer 11

Is 11 hours correct? @tkhunny

Answer 12

That's better, but it's still slower than one of them alone. Ralph can do it by himself in 10 hours. Why would Steve helping slow him down?

The difficult with this problem type is you have the wrong kind of data.

Steve can paint the house in 12 hours.
Ralph can paint the house in 10 hours.

This can also be said:


Steve can paint the 1/12 house in 1 hour.
Ralph can paint the 1/10 house in 1 hours.

You have to get the rates on the same basis. 10 and 12 are just not the same, so it is quite confusing.

NOW they add just fine.

Working together, they cann accomplish 1/12 + 1/10 of the job in 1 hour.

1/10 + 1/12 = (12+10)/120 = 11/60 = 0.1833...

How long will it take to finish. 60/11 = 5.45... hours.

Are we making any sense at all?

Answer 13

Now it is making a lot more sense but now how do I do the original problem where there is an unknown time? @tkhunny

Answer 14

Theorize: Matthew can complete the task, by himself, in M hours.
Time: Wow, they completed the entire task together in only E hours.

Then, \(\dfrac{1}{14} + \dfrac{1}{11} + \dfrac{1}{M} = \dfrac{1}{E}\)

Time to find E.
Solve to find M.

Answer 15

So i simplify that and get \[\frac{ 1 }{ M }+\frac{ 25 }{ 145 }=\frac{ 1 }{ E }\] @tkhunny

Answer 16

?? First, \(\dfrac{1}{14}+\dfrac{1}{11} = \dfrac{25}{154}\)

Second, I suppose that's simplified.

Answer 17

Yeah, I typed that wrong that is what I meant, and so how do I get my answer from that? @tkhunny

Answer 18

Go re-read the problem statement. The problem is for YOU to describe how you would do it. You ahve the formulation and a lovely equation. Now, how would you solve it? Hint: Get a stopwatch.

Answer 19

Now, I see I was trying to solve it myself when I didn't have the value of E which is needed. Thank you so much for your help not only did you lead me in the right direction you used examples and taught me.

Answer 20

@tkhunny

Answer 21

SWEET!!! Good work.