An experienced bricklayer can construct a small wall in 33 hours. An apprentice can complete the job in 77 hours. Find how long it takes if they work together.

Question

An experienced bricklayer can construct a small wall in 33 hours. An apprentice can complete the job in 77 hours. Find how long it takes if they work together.

Answer 1

Bricklayer takes 33 hours to construct the wall.  Per hour he constructs 1/33 wall.

Apprentice takes 77 hours to construct the wall.  Per hour he constructs 1/77 wall.

Working together it takes x hours.  Per hour they construct 1/x of the wall.

 

Set up the equation:

Wall constructed by the bricklayer per hour + Wall constructed by the apprentice per hour = Wall constructed per hour when they work together.

 

1/33 + 1/77 = 1/x

 

7/231 + 3/231 = 1/x

 

10/ 231 = 1/x

 

x = 231/10

 

x = 23.1 

 

It takes 23 hours and 0.1 hour.  Convert 0.1 hour to minutes:

 

0.1 hour x 60min/1hour = 6 min.

 

It takes 23 hours and 6 minutes if they working together.