Question

For a certain bathtub, it takes the cold water faucet 4 times as long to fill the tub as it does the hot water faucet. Left on together, the two faucets take 4minutes to fill the tub. How long will it take the cold water faucet to fill the tub by itself?Do not do any roundingminutes

Answer 1

Let the time taken by the hot water faucet be represented as H,

Let the time taken by the cold water faucet be represented as C.

Since it takes the cold water faucet 4 times as long to fill the tub as it does the hot water faucet, we can imply that

$H\text{ = 4C ----- equation 1}$

When the two faucets are left together, the total time taken is 4 minutes.

Thus,

$\frac{1}{C}+\frac{1}{H}=\frac{1}{4}\text{ ----- equation 2}$

From equation 1, we thus have

$\frac{1}{C}+\frac{1}{4C}=\frac{1}{4}$

Multiply through by 4C, we have

$\begin{gathered} 4C(\frac{1}{C}+\frac{1}{4C})=4C(\frac{1}{4}) \\ \Rightarrow4+1\text{ = C} \\ \text{Thus,} \\ C=5 \end{gathered}$

Thus, the total time taken by the cold water faucet to fill up the tub is 5 minutes.