One inlet pipe can fill an empty pool in 4 hours, and a drain can empty the pool in 8 hours. how long will it take the pipe to fill the pool if the drain is left open?

Given that one inlet pipe can fill an empty pool in 4 hours. The outlet pipe can empty the pool in 8 hours. We know that rate x time = work done.

Rate = work done / time

Rate of inlet pipe = ¼ hours.

Rate of outlet pipe = 1/8 hours

Here 1 represent the work completed.

Let x be the time taken to fill the pool by the inlet pipe if the drain is left.

Work done by inlet pipe – work done by outlet pipe = 1 work completed.

x/4 – x/8 = 1.

To solve the rational equation, first we clear the fractions by multiplying it with LCD (4,8)=8 to each item.

8(x/4) – 8(x/8) = 8(1)

2x – x = 8

X = 8

Time taken for the pipe to fill the pool if the drain is left open = 8 hours

Part A:

Linear function

Part B:

House 1; f(x) = 7595.3·x + 178515

House 2; f(x) = 11,000·x + 179000

Part C:

Yes, there will be a significance difference

The value of house 1 after 30 years is $406,374

The value of house 2 after 30 years is $509,000

Step-by-step explanation:

The given values are

               House 1

Year 1,    186,160

Year 2,   193606.40

Year 3,   201350.66

We see that the prices of the houses have a common difference given as follows;

201,350.66 - 193606.40 = 7744.26,

193,606.40 - 186,160 = 7446.4

Which is fairly constant giving a linear function of the house after a fixed number of years

               House 2

Year 1,    190,000

Year 2,   201,000

Year 3,   212,000

We see that the prices of the houses have a common difference given as follows;

212,000 - 201,000 = 11,000,

201,000 - 190,000 = 11,000

Which is fairly constant

Which is fairly constant giving a linear function of the house after a fixed number of years

Part B:

The function for the first house  is given by the regression formula from regression analysis

Y = a + b·X

Where:

X = Value of the house at Year Y

Y = The year

Which gives;

f(x) = 7595.3·x + 178515

The function for the first house  is given by the arithmetic progression also by regression analysis as follows;

f(x) = 11,000·x + 179000

Part C

The value of house 1 after 30 years = 7595.3×30 + 178515 = $406,374

The value of house 2 after 30 years = 11,000×30 + 179000 = $509,000

Yes, there will be a significance difference between house 2 and house 1 to about 509,000 - 406,374 = $102,626.