Word problem involving Bob and James finishing the roof of a house

Question

Bob and James are finishing the roof of a house. Working alone, Bob can shingle the roof in 14 hours. James can shingle the same roof in 18 hours. How long will it take them working together to shingle the roof? Round your answer to the nearest hundredth if necessary.

Answer 1

Hi Marian,

 

If Bob can do it alone in 14 hours then he can do 1/14 of the job each hour

 

James can do 1/18 of the job each hour.

 

let x = time it takes them working together

 

then

 

x/14 + x/18 = 1    (this statement says that the number of hours x times Bob's rate and James's rate added will give 1 or the full job

 

18x + 14x = 252

 

32x = 252

 

x = 7.875 hours  (time to finish when working together

 

Hope this helps