Question 827737
Set t = Ted's rate as houses per minute
    b = Burt's rate as houses per minute

(t Ted's rate)/( 1 minute ) = (1 house)/( 40 minutes )

{{{t/1 = 1/40}}} 
cross products gives us
40t = 1
divide each side by 40
 t = 1/40 in terms of houses per minute

{{{b/1 = 1/40}}} 
cross products gives us
30b = 1
divide each side by 40
 b = 1/30 in terms of houses per minute

rate * time = houses
( 1/40 + 1/30 )* x = 1 where x is the amount of time
( 1/40 + 1/30 )* x = 1
using common denominator 120
( 3/120 + 4/120 ) * x = 1
( 7/120 )*x = 1
multiply each side by 120/7
 x = 1*(120/7)
 x = 17.14 minutes