Question

It takes the hot water faucet twice as long to fill a bathtub as it does the cold water faucet. Left on together, the cold and hot water faucet take 5 min to fill the tub. How long will it take the cold water faucet to fill itself?

Answer 1

Answer:

Step-by-step explanation:

Make a system of equations

Give the hot and cold faucets variables

Set x to be the minutes it takes for the hot water faucet to fill up the tub and Set y to be the minutes it takes for the cold water faucet to fill up the tub

She first equation is x = 2y because the hot faucet takes 2 times as much time as the cold water

The second equation is x + y = 5 because if you add the number of minutes each takes to fill a tub, it will add up to 5 minutes

Now you have the equations

x = 2y

x + y = 5

So you can plug the first equation in for x in the second one to make

2y + y = 5

which equals 3y = 5

Then you divide 3 from both sides to get

y = $\frac{5}{3}$

Since y is the number of minutes the cold water faucet takes to fill the tub, then the cold faucet takes $\frac{5}{3}$ minutes for the cold water faucet to fill the tub itself