Question 593189
Let T = Tom's time
Then Joe's time = T + 10
Working together their work rate is 1/12, so we can write
1/T + 1/(T+10) = 1/12
((T+10) + T)/(T(T+10)) = 1/12
Simplify and solve:
T^2 - 14T - 120 = 0
Factor:
(T-20)(T+6) = 0
Take the positive solution, T=20
That means it takes Joe 30 hours to do his homework.