Using my faucet, it takes 6 minutes to fill our water tank. Using my neighbor's hose, it takes 9 minutes. How long would it take if i used both the faucet and the hose?
1/6 + 1/9 = x
3/18 + 2/18 = x
x = 5/18 * 1
x = 18/5
x = 3.6 minutes
use this formula
t/a+t/a=1
where t=together and a=alone
x/6 + x/9 = 1
(6x+9x)/54 =1
15x=54
x=54/15
x=3 3/5 minutes = 3minutes 36 seconds
3 minutes 36 seconds. but i don't know why
Well, if the faucet and the hose teamed up, I think they would need some serious couples counseling! But let's do some math instead.
If it takes 6 minutes to fill the water tank with just the faucet, and 9 minutes with just the hose, we can tell that the faucet is faster at filling the tank. So, let's say the faucet can fill the tank in 1 minute, and the hose takes 1.5 minutes.
When they work together, it's like a superhero team-up! The faucet can fill 1 tank in 1 minute, and the hose can fill 1 tank in 1.5 minutes. So, together, they can fill 1 tank in 1 + 1.5 = 2.5 minutes!
So, if you used both the faucet and the hose, it would take approximately 2.5 minutes to fill your water tank. Teamwork makes the dream work, right?
To find out how long it would take to fill the water tank using both the faucet and the hose, we can calculate their combined filling rates.
First, let's find the filling rate of your faucet. Since it takes 6 minutes to fill the water tank using your faucet alone, we can say that your faucet fills 1/6 (one sixth) of the tank per minute.
Similarly, your neighbor's hose takes 9 minutes to fill the water tank, meaning it fills 1/9 (one-ninth) of the tank per minute.
To calculate their combined filling rate, we can add the rates from both sources: 1/6 + 1/9. We need to find a common denominator, which in this case is 18, so the equation becomes 3/18 + 2/18.
Adding the numerators gives us 5/18. Therefore, the combined filling rate is 5/18 of the tank per minute.
To determine the time it would take to fill the water tank using both the faucet and the hose, we can take the reciprocal of the combined filling rate (18/5) and simplify it to get the answer.
Dividing 18 by 5 results in 3 remainder 3, so the answer is 3 and 3/5 minutes.
Therefore, it would take approximately 3 minutes and 36 seconds to fill the water tank using both the faucet and the hose.