Question

It takes Trevon ten hours to clean an attic.
Cody can clean the same attic in seven
hours. Find how long it would take them if
they worked together

Answer 1

Rate that Trevon can clean an attic = T= 1 attic/10hrs
Rate that Cody can clean an attic = C= 1 attic/7hrs
t = time it takes (in hours) for both of them together to clean 1 attic
1 = T*t + C+t, because in t hours, both of them working together will clean 1 attic
solve for t -- that's it.

Answer 2

T = hours it takes Trevon to clean attic = 10
C = hours it takes Cody to clean attic = 7

Then the time it takes both to clean the attic while working together is represented by:

\[\frac{CT}{C + T} = t\]

Solving for t...
\[\frac{(7)(10)}{7 + 10} = \frac{70}{7} = 4\frac{2}{17}\text{hours}\]