Question

Painting. Quentin can paint the turret on a Queen Anne house in 40 hr. It takes Austin 50 hr to paint the same turret. How long would it take them, working together, to paint the turret?

Answer 1

The answer to your question is 22.2 hours

Explanation:

Data

Quentin 40 hr to paint a turret

Austin 50 hr to paint a turret

Use proportions to solve this problem

Quentin 1 turret ---------------- 40 hr Austin 1 turret --------------- 50 hr

x ---------------- 1 hr x ---------------- 1 hr

x = 0.025 turret x = 0.02 turret

Then

- In 1 hour they paint 0.025 + 0.02 = 0.045 of the turret

- In 10 hours they paint (10 x 0.025 + 10 x 0.02) = 0.25 + .2 = 0.45

- In 20 hours they paint (20 x 0.025 + 20 x 0.02) = 0.5 + 0.4 = 0.9

- In 22 hours they paint (22 x 0.025 + 22 x 0.02) = 0.55 + 0.44 = 0.99

- In 22.2 hours they paint (22.2 x 0.025 + 22.2 x 0.02) = 0.555 + .0.444 =

0.999

They paint the turret together in 22.2 hours