Answer:
Let's define 1 as a complete one task, in this case, the complete task is shingle the roof.
Also, let's define the variables:
B = Rate at which Bob can complete one task.
J = Rate at which James can complete one task.
Then we have two equations:
"Working together they can shingle the house in 5 hours and 30 minutes."
(i will use 5 hours and 30 minutes = 5.5 hours)
(B + J)*5.5h = 1.
"Bob can shingle the roof in 17 hours. "
B*17h = 1.
In the second equation, we can find the value of B.
B = 1/17h
Now we can replace it in the first equation, and get:
(1/17h + J)*5.5h = 1
(1/17h + J) = 1/5.5h
J = 1/5.5h - 1/17h
And that is the rate at which James can complete the work, then the time that James needs is 1/J
Time = 1/( 1/5.5h - 1/17h) = 8.13 hours.
