10. a house painter can finish a house in 6 hours. his partner can finish the same house in 12 hours. which of the
following is the number of hours it would have taken them to finish painting the house if they had worked together?
a. 3 hours b. 4 hours c. 6 hours d. 9 hours

I got B. 4 hours.

Step-by-step explanation:

1. Find the unit rate of both painters. So in 1 hour, the painter finishes 1/6 of the house. In 1 hour the partner finishes 1/12th of the house.

2. A completed house equals 1.

3. Putting it all together you get: 1/6+1/12=1. Since we want to know the number of hours, x is in the numerator. Giving x/6 + x/12 =1.

4. Multiply by 12 to get common denominator for the whole equation, you get 2x +x =12. Solve for x you get 4.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

it has changed from the width and the height.

step-by-step explanation: