how long must they work to paint the fence?

Question

It takes Ralph 7 hours to paint a fence alone. Lisa can do the same job in 11 hours. If Ralph paints alone for 15 minutes before Lisa begins helping, how long must they work together to finish painting the fence?

Answer 1

In one hour Ralph paints 1/7 of the fence.

In one hour Lisa paints 1/11 of the fence

 

In x hours, Ralph paints x/7 of the fence

In x hours, Lisa paints x/11 of the fence

 

Yet Ralph paints for 0.25 hours more

 

(x + 0.25) / 7 + x / 11 = 1                Each does a fraction of the 1 job.

 

11(x + 0.25) + 7x = 77                     Multiply by 77 the common denominator

11x + 2.75 + 7x = 77

18x + 2.75 = 77

18x = 74.25

x = 4.125

 

The finish the job is 4.125 hours.