Bob and James are finishing the roof of a house. Working alone, Bob can shingle the roof in 10 hours. James can shingle a roof in 16 hours.

Question

Bob and James are finishing the roof of a house. Working alone, Bob can shingle the roof in 10 hours. James can shingle a roof in 16 hours. How long will it take them working together to shingle the roof. Round your answer to the nearest hundredth.

Answer 1

Bob can shingle 1 roof for every 10 hours of work. (1/10)

James can shingle 1 roof for every 16 hours of work. (1/16)

To find out what they can do together, you must add their rates of work together.

This will be the number to find how fast they can shingle 1 roof in t amount of hours (1/t)

 

1/10 + 1/16 = 1/t

 

8/80 + 5/80 = 1/t

 

13/80 = 1/t

 

Cross multiply

 

13(t) = 1(80)

 

13t = 80

 

t = 6.15

 

It would take them 6.15 hours to complete the roof together.