Roofing a home

Question

 

One roofing crew can finish a 2,800-sqaure-foot roof in 12 hours, and another crew can do the job in 10 hours. If they work together, can they finish before a predicted rain in 5 hours?

Answer 1

If they work together it will take X - hours to finish

 

 

 1/ 10 + 1/12 = 1/x

 

  6/ 60 + 5/ 60 = 1/X

 

   11/ 60 = 1/x

 

   X = 60/11 = 5 45/99 = 5 5/11  the amount of time needed to finish working together, that is 5/11 hour   more than needed.  

Answer 2

Start by figuring out how much work each crew can finish in one hour on their own (assuming a consistent level of work across the entire job).

 

So, if Crew 1 can finish 2,800 sq.ft. in 12 hours, they can finish 233 1/3 sq.ft. in one hour (2800/12).

 

And, if Crew 2 can finish 2,800 sq. ft. in 10 hours, they can finish 280 sq. ft. in one hour (2800/10).

 

Combined they can finish 513 1/3 sq. ft. in one hour (233 1/3 + 280).

 

Can they finish the job in 5 hours? Multiply 513 1/3 * 5 = 2,566 2/3 sq. ft.

 

Since 2566 2/3 < 2800, no, they cannot finish the job before the predicted rain.