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vfiekz [6]
3 years ago
14

A family of five recently replaced its 5-gallon-per-minute shower heads with water-saving 2-gallon-per-minute shower heads. Each

member of the family averages 8 minutes in the shower per day. In a 30-day period, how many fewer gallons of water will the family use with the new shower heads?
a. 60.
b. 800.
c. 2400.
d. 3600.
e. 7200.
Mathematics
1 answer:
Anna [14]3 years ago
5 0

Answer:

Option d.

Step-by-step explanation:

Number of family members = 5

Average time for shower = 8 minute per member

Time period = 30

Initial rate of water = 5-gallon-per-minute

Initial use of water is

5\times 8\times 30\times 5=6000

New rate of water = 2-gallon-per-minute

Use of water after new shower is

5\times 8\times 30\times 2=2400

Difference between use of water is

6000-2400=3600

It means the family will use 3600 fewer gallons of water with the new shower heads.

Therefore, the correct option is d.

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\begin{array}{rcl}A& =&\dfrac{10}{1+ kt}\\\\4 & =& \dfrac{10}{1 + 10k}\\\\4 + 40 k & = & 10\\\\40k & = & 6\\k & = & 0.15\\\end{array}\\\\\mathbf{A} =\mathbf{ \dfrac{10}{0.15t + 1}}

(ii) Find t when A < 1

\begin{array}{rcl}A(t) & < & 1\\\dfrac{10}{0.15t + 1} & < & 1\\\\10 & < & 0.15t + 1\\9 & < & 0.15t\\t & > & 60\\\\\end{array}\\\mathbf{A < 1} \textbf{ when }\mathbf{ t >60}

The figure below shows the graph of A vs t.

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