Question

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

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.

Answer 2

The formula for this is:
Total time = (Worker1 * Worker2) / (Worker1 + Worker2)
Total time = (10 * 16) / (10 + 16)
Total time = 160 / 26
Total time = 6.1538461538 = 
Total time = 6.15 Hours (rounded to nearest hundredth).

Source:
http://www.1728.org/work.htm