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 answer is thin because within context, the stanza concludes the and frail tone the people have toward each other, and the fact that it would be thin, makes the most sense compared to "pliable" or "not hard or firm to the touch". hope this , good luck.

step-by-step explanation:

can i have brainliest

the diameter is 16 cm. are you a teacher?

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