Question

the two longest total solar eclipses occurred in 1991 and 1992. the first one lasted $6\frac{5}{6}$ minutes. the eclipse of 1992 lasted $5\frac{1}{3}$ minutes. how much longer was 1991’s eclipse?

Explanation:

Step1: Convert mixed numbers to improper fractions

The duration of the 1991 eclipse is \( 6\frac{5}{6} = \frac{6\times6 + 5}{6}=\frac{41}{6} \) minutes.
The duration of the 1992 eclipse is \( 5\frac{1}{3}=\frac{5\times3+1}{3}=\frac{16}{3} \). We need to have a common denominator, so rewrite \( \frac{16}{3} \) as \( \frac{32}{6} \).

Step2: Subtract the two durations

To find how much longer the 1991 eclipse was, we subtract the duration of the 1992 eclipse from the 1991 one: \( \frac{41}{6}-\frac{32}{6}=\frac{41 - 32}{6}=\frac{9}{6} \).

Step3: Simplify the result

Simplify \( \frac{9}{6} \) to \( \frac{3}{2} \), which is \( 1\frac{1}{2} \) minutes.

Answer:

\( 1\frac{1}{2} \) minutes (or \( \frac{3}{2} \) minutes)