Two painters can paint a room in 2 hours if they work together. the inexperienced painter takes 3 hours more than the experienced painter to finish the job. how long does it take for each painter to paint the room individually?

The experienced painter takes 3 hours to paint the room

The inexperienced painter takes 6 hours to paint the room

Step-by-step explanation:

* Lets explain how to solve the problem

- Two painters can paint a room in 2 hours if they work together

- Assume that the experienced painter can paint the room in a hours

∴ Its rate is 1/a

- Assume that the inexperienced painter can paint the room in b hours

∴ Its rate is 1/b

∵ When they working together they will finish it in two hours

∴ Their rate together is 1/2

- Equate the sum of the rate of each one and the their rate together

∴

-To add two fraction with different denominators we multiply the 2

 denominators and multiply each numerator by the opposite

 denominator

∴

- By using the cross multiplication

∴ 2(b + a) = ab

∴ 2b + 2a = ab ⇒ (1)

- The inexperienced painter takes 3 hours more than the experienced

  painter to finish the job

∵ The experienced painter can finish the room in a hours

∵ The inexperienced painter can finish the room in b hours

∵ The inexperienced painter takes 3 hours more than the experienced

  painter to finish the job

∴ b = a + 3 ⇒ (2)

- Substitute equation (2) in equation (1)

∴ 2(a + 3) + 2a = a(a + 3)

∴ 2a + 6 + 2a = a² + 3a ⇒ add like terms

∴ 4a + 6 = a² + 3a ⇒ subtract 4a from both sides

∴ 6 = a² - a ⇒ subtract 6 from both sides

∴ a² - a - 6 = 0 ⇒ factorize it

∵ a² = (a)(a)

∵ -6 = -3 × 2

∵ -3(a) + 2(a) = -3a + 2a = -a ⇒ the middle term in the equation

∴ a² - a - 6 = (a - 3)(a + 2)

∵ a² - a - 6 = 0

∴ (a - 3)(a + 2) = 0

∴ a - 3 = 0 ⇒ add 3 to both sides

∴ a = 3

- OR

∴ a + 2 = 0 ⇒ subtract 2 from both sides

∴ a = -2 ⇒ rejected because there is no negative value for the time

- Substitute the value of a in equation (2) to find b

∵ b = 3 + 3 = 6

∴ The experienced painter takes 3 hours to paint the room

∴ The inexperienced painter takes 6 hours to paint the room

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation:

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct