A pool contains 50 gallons of water and is filling at a rate of 2.3 gallons per minute. A second pool contains 102.2 gallons of water and is draining at a rate of 3.5 gallons per minute. After how many minutes will the pools contain the same amount of water?

The pools will contain same amount of water in 9 minutes

Let the number of minutes that the pools contain the same amount of water be represented by t.

Since the first pool contains 50 gallons of water and is filling at a rate of 2.3 gallons per minute, then this will be:

= 50 + (2.3 × t)

= 50 + 2.3t equation i

The second pool contains 102.2 gallons of water and is draining at a rate of 3.5 gallons per minute. This will be:

= 102.2 - (3.5 × t)

= 102.2 - 3.5t equation ii

Equate both equations and this will be:

50 + 2.3t = 102.2 - 3.5t

Collect like terms

2.3t + 3.5t = 102.2 - 50

5.8t = 52.2

Divide both side by 5.8

5.8t/5.8 = 52.2/5.8

t = 9

In conclusion, they'll have same amount of water in 9 minutes

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At time t, the first pool contains 50+2.3t gal of water, while the second pool contains 102.2-3.5t gal.

They contain the same amount of water when these quantities are equal:

50 + 2.3t = 102.2 - 3.5t

5.8t = 52.2

t = 9

so the pools have the same amount of water after 9 min have passed.

explanation:

step-by-step explanation:

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.