Answer: 19/72 of the tank of fuel remaining
Explanation:
To find out what fraction of the tank of fuel remains, we need to subtract the fractions of the tank that Bill used from the initial fraction.
Bill starts with 3/4 of a tank of fuel. In the morning, he uses 1/9 of the tank, and in the afternoon, he uses 3/8 of the tank.
So, the fraction of the tank used in the morning and afternoon combined is:
1/9 (morning) + 3/8 (afternoon)
To add these fractions, we need a common denominator, which is the least common multiple of 9 and 8, which is 72. Now, we'll rewrite the fractions with a denominator of 72:
(1/9) * (8/8) = 8/72
(3/8) * (9/9) = 27/72
Now, we can add these fractions:
(8/72) + (27/72) = (8 + 27) / 72 = 35/72
So, Bill used a total of 35/72 of the tank during the day.
To find out what fraction of the tank remains, subtract this from the initial 3/4 of the tank:
3/4 (initial) - 35/72 (used) = ?
To subtract these fractions, we need a common denominator of 72:
(3/4) * (18/18) = 54/72
Now, subtract:
(54/72) - (35/72) = (54 - 35) / 72 = 19/72
So, Bill has 19/72 of the tank of fuel remaining.