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A faucet is leaking at the rate of 9 deciliters, 9 centiliters, and 2 milliliters per hour. How much water will leak out after 3 hours?

Give a decimal answer in liters.

Answer :

The faucet leaks water at three different rates per hour. We first convert each rate to liters:

1. Deciliters to liters:
 Since [tex]$1$[/tex] deciliter equals [tex]$0.1$[/tex] liter,
 [tex]$$9 \text{ deciliters} = 9 \times 0.1 = 0.9 \text{ liters}.$$[/tex]

2. Centiliters to liters:
 Since [tex]$1$[/tex] centiliter equals [tex]$0.01$[/tex] liter,
 [tex]$$9 \text{ centiliters} = 9 \times 0.01 = 0.09 \text{ liters}.$$[/tex]

3. Milliliters to liters:
 Since [tex]$1$[/tex] milliliter equals [tex]$0.001$[/tex] liter,
 [tex]$$2 \text{ milliliters} = 2 \times 0.001 = 0.002 \text{ liters}.$$[/tex]

Next, we add these amounts to find the total leakage per hour:
[tex]$$
\text{Leakage per hour} = 0.9 + 0.09 + 0.002 = 0.992 \text{ liters per hour}.
$$[/tex]

Since the faucet leaks for [tex]$3$[/tex] hours, the total amount of water leaked is:
[tex]$$
\text{Total leakage} = 0.992 \times 3 = 2.976 \text{ liters}.
$$[/tex]

Thus, after [tex]$3$[/tex] hours, a total of [tex]$2.976$[/tex] liters of water will have leaked.

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