Question
You have \( \frac{3}{4} \) of a tank of fuel to power a compressor that uses \( \frac{1}{8} \) tank per hour. If you work 3 hours in the morning (using \( \frac{3}{8} \) of a tank) and 2 hours in the afternoon (using \( \frac{2}{8} \) of a tank), how much of the tank remains? Yout answer should be in the form of a fraction reduced to its lowest terms. The tank is now \( \square \) full.
Ask by Chan Campbell. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The tank is now \( \frac{1}{8} \) full.
Solution
We start with ¾ of a tank. In the morning, 3 hours of work uses 3 × (1/8) = 3/8 of a tank, and in the afternoon, 2 hours uses 2 × (1/8) = 2/8 of a tank. Together, the total fuel used is 3/8 + 2/8 = 5/8 of a tank.
Subtracting the used fuel from the initial fuel:
3/4 – 5/8 = 6/8 – 5/8 = 1/8.
Thus, the tank is now 1/8 full.
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Simplify this solution Extra Insights
You start with \( \frac{3}{4} \) of a tank. After working 3 hours in the morning, you use \( \frac{3}{8} \) of a tank, which leaves you with: \[ \frac{3}{4} - \frac{3}{8} = \frac{6}{8} - \frac{3}{8} = \frac{3}{8} \] In the afternoon, you work for 2 more hours and use \( \frac{2}{8} \) of a tank, resulting in: \[ \frac{3}{8} - \frac{2}{8} = \frac{1}{8} \] So, the tank is now \( \frac{1}{8} \) full.
