for a certain bathtub, it takes the hot water faucet 3 times as long to fill the tub as it does the cold water faucet. left on together, the two faucets take 6 minutes to fill the tub. how long will it take the hot water faucet to fill the tub by itself?

Let h and c be times for each faucet.
h = 3c

The rate is equal to inverse of time.
1/c = rate of bathtub per minute that cold faucet is filling up bath

When both faucets are on, you add the rates together.
Since time is 6 min, the rate of water must equal 1/6

[tex]\frac{1}{h} + \frac{1}{c} = \frac{1}{6}[/tex]

Sub in 3c for h
solve for c

[tex]\frac{1}{3c} + \frac{1}{c} = \frac{1}{6} \\ \\ \frac{4}{3c} = \frac{1}{6} \\ \\ 3c = 24 \\ \\ c = 8[/tex]

h = 3c = 24

It takes hot faucet 24 min to fill bath.

johanrusli johanrusli · Answer 2 · 2019-09-11T03:45:58+02:00

It take 24 minutes for the hot water faucet to fill the tub by itself

Further explanation

This problem is related to the speed of the water flow.

To solve this problem, we must state the formula for the speed.

[tex]\large {\boxed {v = \frac{V}{t}} }[/tex]

where:

v = speed of water flow ( m³ / s )

V = volume of water ( m³ )

t = time taken ( s )

Let's tackle the problem!

For a certain bathtub, the cold water faucet can fill the tub in t_c minutes.

[tex]\text{Cold Water Flow Speed} = v_c = Volume \div t_c[/tex]

The hot water faucet can fill the tub in t_h minutes.

[tex]\text{Hot Water Flow Speed} = v_h = Volume \div t_h[/tex]

It takes the hot water faucet 3 times as long to fill the tub as it does the cold water faucet.

[tex]t_h = 3 \times t_c[/tex] → Equation 1

If both faucets are used together , the two faucets take 6 minutes to fill the tub ( t = 6 minutes )

[tex]\text{Total Water Flow Speed} = v = v_c + v_h[/tex]

[tex]\frac{Volume}{t} = \frac{Volume}{t_c} + \frac{Volume}{t_h}[/tex]

[tex]\frac{1}{t} = \frac{1}{t_c} + \frac{1}{t_h}[/tex]

[tex]\frac{1}{t} = \frac{1}{t_c} + \frac{1}{3t_c}[/tex] ← Equation 1

[tex]\frac{1}{6} = \frac{3}{3t_c} + \frac{1}{3t_c}[/tex]

[tex]\frac{1}{6} = \frac{4}{3t_c}[/tex]

[tex]3t_c = 4 \times 6[/tex]

[tex]3t_c = 24[/tex]

[tex]t_c = 24 \div 3[/tex]

[tex]t_c = 8 ~ \text{minutes}[/tex]

[tex]t_h = 3 \times t_c[/tex]

[tex]t_h = 3 \times 8[/tex]

[tex]t_h = 24 ~ \text{minutes}[/tex]

Learn more

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Water , Flow , Speed , Bathtub