Question

Clarissa and Shawna, working together, can paint the exterior of a house in 6 days. Clarissa by herself can complete this in 5 days less than Shawna. how long will it take Clarissa to complete the job by herself?

Answer 1

Clarissa will take 10 hours by herself

Explanation:

Let s = time for shawna

s-5 = time for clarissa

The formula for determining the time is

1/a + 1/b = 1/c where a and b are the times alone and c is the time together

1/s + 1/(s-5) = 1/6

Multiply each side by 6s(s-5) to clear the fractions

6s(s-5) ( 1/s + 1/(s-5)) = 1/6 *6s(s-5)

Distribute

6(s-5) + 6s = s(s-5)

Distribute

6s -30 +6s = s^2 -5s

Combine like terms

12s -30 = s^2 -5s

Move everything to the right

0 = s^2 -5s -12s +30

0 = s^2 -17s +30

Factor

0 = ( s-15) (s-2)

Using the zero product property

s-15 =0 s-2 =0

s =15 s=2 ( This is not a reasonable answer since it is less than the time together)

s=15

s-5 = 10

Clarissa will take 10 hours by herself