Final answer:
Sam mows his lawn and washes his car on the same day in 45 days.
Step-by-step explanation:
To find the number of days until Sam mows his lawn and washes his car on the same day, we need to find the least common multiple (LCM) of 9 and 15.
The LCM is the smallest multiple that both 9 and 15 have in common.
Prime factorizing 9:
=> 9 = 3 x 3
Prime factorizing 15:
=> 15 = 3 x 5
The LCM of 9 and 15 is the product of the highest powers of all prime factors involved, which is 3 x 3 x 5 = 45.
Therefore, it will be 45 days until Sam mows his lawn and washes his car on the same day.