Dana can paint a barn in 5 hours while Giovanni paints the same size barn in 8 hours. How long will it take to paint the barn if they worked together?

Question

 Please help! I am having some trouble solving this problem.

Answer 1

Think about this

Dana (d) paints a barn in 5 hours, so her rate of work is :

1/5 of a barn (b) in 1 hour, so set d =1/5b

 

Giovanni (g) paints a barn in 8 hours, so his rate of work is:

1/8 of  a barn in 1 hour, so set g=1/8b

 

Now we want to know what happens when we combine Dana and Giovanni's hourly rates.

we have :

d+g = 1 hour of Dana and Giovanni's work

1b/5+1b/8=1

 

combine the fractions 

 

8b/40 + 5b/40=1

 

13b/40=1 This is the combined rate of work for Dana and Giovanni. 

 

Now just find b

 

b=40/13 

 

thus it will take 40/13 hours of work to paint a barn if Dana and Giovanni do it together.

 

Answer 2

t represents the time for both to paint

t/3 + t/8 = 1

 

Can you solve for t and answer?