A plane is at an altitude of 20683 2/3 feet above ground level. After 30 minutes, the plane rises by an altitude of 6733 3/8 feet. Which of the following is true about the altitude of the plane after 30 minutes?

Question

A.
The altitude of the plane after 30 minutes is -27417 1/24feet.
B.
The altitude of the plane after 30 minutes is 13951 1/24feet.
C.
The altitude of the plane after 30 minutes is 27417 1/24 feet.
D.
The altitude of the plane after 30 minutes is -13951 1/24 feet.

Answer 1

To find the altitude of the plane after 30 minutes, we need to add the initial altitude and the increase in altitude.

The initial altitude is: \[ 20683 \frac{2}{3} \text{ feet} \]

To add these fractions, we first convert \( 20683 \frac{2}{3} \) to an improper fraction: \[ 20683 \frac{2}{3} = \frac{20683 \times 3 + 2}{3} = \frac{62049 + 2}{3} = \frac{62051}{3} \text{ feet} \]

Next, we convert the increase in altitude, \( 6733 \frac{3}{8} \), to an improper fraction as well: \[ 6733 \frac{3}{8} = \frac{6733 \times 8 + 3}{8} = \frac{53864 + 3}{8} = \frac{53867}{8} \text{ feet} \]

Now, we need to add these two improper fractions: \[ \frac{62051}{3} + \frac{53867}{8} \]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 3 and 8 is 24.

Now we convert each fraction: \[ \frac{62051}{3} = \frac{62051 \times 8}{24} = \frac{496408}{24} \] \[ \frac{53867}{8} = \frac{53867 \times 3}{24} = \frac{161601}{24} \]

Now we can add the two fractions: \[ \frac{496408}{24} + \frac{161601}{24} = \frac{496408 + 161601}{24} = \frac{658009}{24} \]

Now, to see what this mixed fraction is, we can divide: \[ 658009 \div 24 \approx 27417 \frac{1}{24} \]

Thus, the altitude of the plane after 30 minutes is: \[ 27417 \frac{1}{24} \text{ feet} \]

So the correct answer is: C. The altitude of the plane after 30 minutes is \( 27417 \frac{1}{24} \) feet.