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

Answer: 6.15 hours

=========================================================

Work Shown:

x = amount of time it takes for Bob to do the job alone

x = 10 hours

y = amount of time it takes for James to do the job alone

y = 16 hours

z = amount of time it takes for them to work together

z = (x*y)/(x+y)

z = (10*16)/(10+16)

z = 160/26

z = 6.1538 approximately

z = 6.15

They will take about 6.15 hours if they work together, and if neither person slows the other down.

-------------------

Another approach (optional section):

Let's say there are 80 shingles needed to cover the roof.

If Bob needs 10 hours when working alone, then his rate is 80/10 = 8 shingles per hour.

If James needs 16 hours when working alone, then his rate is 80/16 = 5 shingles per hour.

Their combined rate is 8+5 = 13 shingles per hour.

h = number of hours they work together

13h = number of shingles they can do after h number of hours

13h = 80

h = 80/13

h = 6.15 approximately

We get the same answer as before.

Answer 2

This should be correct

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.