Sophie does 1/45 of the job in one minute and Simon does 1/30 of the job in one minute.....let x be the time it takes to do the job [in minutes] working together....and we have......
(1/45)x + (1/30)x = 1 ..... where "1" represents the completed job......getting a common denominator, we have
[30 + 45]x / 1350 = 1 simplify
(75/ 1350)x = 1 multiply both sides by 1350/75 and we have
x = 1350/75 = 18 minutes
