Cleaning orgy in the restaurant kitchen

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Photo: DER SPIEGEL

Anna, Bert and Charlie work in a restaurant kitchen.

Usually there are two of them and the third person is free.

After the kitchen closes, there is still a lot of work waiting for the cooks: They have to clear the ship.

So clean pots, stoves and work surfaces - as well as bowls, knives and other utensils.

Everyone has their own pace.

• When

  Anna

  and

  Bert are on

  duty, they need

  two hours

  cleaning and tidying up.

• It takes Bert

  and

  Charlie

  three hours

  together

  .

• Anna

  and

  Charlie

  need

  four hours

  together

  .

The three of them are on duty together for the first time on a Saturday.

How long do you need to bring the three of you to the kitchen?

Note: We assume that the scope of work is the same every evening.

In addition, each of the three people always works at the same individual speed, regardless of who they are on duty with and how many cooks are on duty together.

Please scroll down to find the solution!

Photo: Michael Niestedt / DER SPIEGEL

solution

The three of them need a total of

24/13 hours

, which corresponds to

one hour, 50 minutes and 46 seconds

.

There are several ways to get this result.

I suggest the following.

With a, b, and c we denote the working speed of Anna, Bert and Charlie per hour.

We call the work to be done A. Then the following equations apply:

2a + 2b = A

3b + 3c = A

4a + 4c = A

We divide all three equations by the number of hours.

The three equations then indicate how much the chefs can do in an hour:

a + b = A / 2

b + c = A / 3

a + c = A / 4

Now we add the three equations and get:

2 (a + b + c) = 13/12 * A

Now we divide both sides by 13/12.

Then on the right is A, i.e. the work to be done by the trio.

And the factor to the left of (a + b + c) indicates how many hours the three need for this:

24/13 * (a + b + c) = A

Many thanks to reader Harry Schmidt for suggesting this puzzle.

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