If both faucets are used together, it will take about 4.55 minutes to fill the tub
Further explanation
This problem is related to the speed of the water flow.
To solve this problem, we must state the formula for the water discharge.
[tex]\large {\boxed {Q = \frac{V}{t}} }[/tex]
where:
Q = water discharge ( 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 7 minute.
[tex]\text{Cold Water Flow Speed} = Q_c = Volume \div t_c[/tex]
[tex]Q_c = Volume \div 7[/tex]
The hot water faucet can fill the tub in 13 minutes.
[tex]\text{Hot Water Flow Speed} = Q_h = Volume \div t_h[/tex]
[tex]Q_c = Volume \div 13[/tex]
If both faucets are used together.
[tex]\text{Total Water Flow Speed} = Q = Q_c + Q_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}{7} + \frac{1}{13}[/tex]
[tex]t = \frac{ 13 \times 7 }{13 + 7}[/tex]
[tex]t = \frac{ 91 }{20}[/tex]
[tex]t = 4.55 ~ \text{minutes}[/tex]
Learn more
- Infinite Number of Solutions : https://brainly.com/question/5450548
- System of Equations : https://brainly.com/question/1995493
- System of Linear equations : https://brainly.com/question/3291576
Answer details
Grade: High School
Subject: Mathematics
Chapter: Discharge
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Water , Flow , Speed , Volume
