How Long Will It Take to Fill Archimedes' Bath Using All Three Taps?

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In summary, there are three taps labelled A, B, and C that are used to fill Archimedes' bath. The rate of flow of tap B is twice that of tap A, and the rate of flow of tap C is three times that of tap A. Yesterday, Archimedes filled his bath in two parts: first using all three taps for 2 hours, and then using only taps A and C for an additional 2 hours and 45 minutes. Today, he will fill his empty bath using all three taps. To calculate how long this will take, we can determine the time it takes to fill the bath with just tap A, and then use this information to find the total time for all three taps.
  • #1
Natasha1
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Could I please be explained this problem as I simply can't do it...

Archimedes has a bath which is filled using three taps labelled A, B and C.

The rates of flow of B is twice that of A, the rates of flow of C is three times that of A.

Yesterday, Archimedes filled his bath as follows:

Firstly he used all three taps for 2 hours. Then he turned off B and finished filling the bath in an additional 2 hours and 45 mins using taps A and C only (it's a very big bath).

Today Archimedes is going to fill his bath (currently empty) using all three taps.

How long will this take him?
 
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  • #2
I see that you have 250+ posts so you certainly know by now that you should have posted that in the format of a homework problem and shown some attempt to solve it and where you are stuck. This way folks can see what you know / don't know and try to help you fill in the gap.

Just asking this forum to spoon-feed you a fully worked out answer is not appropriate here.
 
  • #3
Thanks for your help phinds, much appreciated...
 
  • #4
Natasha1 said:
Thanks for your help phinds, much appreciated...

I see you've noticed that sarcasm IS allowed :smile:
 
  • #5
Natasha1 said:
Could I please be explained this problem as I simply can't do it...

Archimedes has a bath which is filled using three taps labelled A, B and C.

The rates of flow of B is twice that of A, the rates of flow of C is three times that of A.

Yesterday, Archimedes filled his bath as follows:

Firstly he used all three taps for 2 hours. Then he turned off B and finished filling the bath in an additional 2 hours and 45 mins using taps A and C only (it's a very big bath).

Today Archimedes is going to fill his bath (currently empty) using all three taps.

How long will this take him?

Have a think about how long "the first part" of the fill would have taken with only tap A. Then have a think about how long "the rest of the fill" would take using just tap A.

Once you know how long it would take using just tap A, it should be pretty easy to calculate how long it would take using all three taps together.
 

FAQ: How Long Will It Take to Fill Archimedes' Bath Using All Three Taps?

What is Archimedes' bath problem?

Archimedes' bath problem is a famous mathematical puzzle that was posed by the Greek mathematician Archimedes. The problem involves determining the volume of an irregularly shaped object by measuring the amount of water it displaces when submerged in a bath.

How did Archimedes solve the bath problem?

Archimedes used a method called the "principle of buoyancy" to solve the bath problem. He realized that the weight of the water that is displaced by an object is equal to the weight of the object itself. By measuring the weight of the displaced water, he could then calculate the volume of the object.

What is the significance of Archimedes' bath problem?

Archimedes' bath problem is significant because it is considered one of the earliest examples of using mathematical principles to solve real-world problems. It also laid the foundation for the development of the concept of buoyancy and the famous Archimedes' principle.

Can the bath problem be applied to other objects?

Yes, the bath problem can be applied to any object, regardless of its shape or size, as long as it can be submerged in water. This method is still used today in various industries, such as shipbuilding and engineering, to determine the volume of irregularly shaped objects.

Is Archimedes' bath problem still relevant today?

Absolutely! The principles and methods used to solve the bath problem are still used in various fields, including mathematics, physics, and engineering. It also serves as a great introduction to the concept of buoyancy and displacement for students studying these subjects.

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