faucet into a fraction or mixed number

Question

a sink can filled by either of two faucets.The first faucet, used alone with the drain stopped can fill the sink in 4 seconds. The second faucent, used alone with the drain stopped, can fill the sink in 15 seconds. If both facuets are open and the drain is closed how many seconds will it take to fill in the sink?

Answer 1

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Answer 2

In x seconds the first faucet fills x/4 of the sink

In x seconds the second faucet fills x/15 of the sink

 

x/4 + x/15 = 1       (1 sink!)

15x + 4x = 60

19x = 60

x ≈ 3.15789

 

The two faucets fill the sink a just over three minutes.

Answer 3

Hi Kami,

 

Let the sink have a volume V. Faucet 1 can fill the sink in 4 sec. So, it has a flow rate of ρ₁ = V/4.

 

Faucet 2 can fill the sink in 15 sec. So, it has a flow rate of ρ₂ = V/15.

 

How long will it take to fill the sink if both faucets are turned on? Let T be this time.

 

(ρ₁ + ρ₂)T = V

 

or specifically

 

(V/4 + V/15)T = V

 

or, factoring out V, we have

 

V(1/4 + 1/15)T = V

 

We can cancel out V from both sides of the equation.

 

(1/4 + 1/15)T = 1

 

Finding a common denominator:

 

(15/60 + 4/60)T = 1

 

or

 

19T/60 = 1

 

or

 

T = 60/19 = 3.2 sec