Questions: The following table lists three upcoming total eclipses of the Sun that will be visible in a certain country. The duration of each eclipse is listed in the table below. How much longer will the March 29 eclipse be than the June 21 eclipse? Total Solar Eclipses Date of Eclipse Duration (in minutes) June 21 3 2/3 March 29 6 7/15 November 3 4 7/20 The March 29 eclipse will be min longer than the June 21 eclipse. (Type an integer, proper fraction, or mixed number. Simplify your answer.)

Solution Steps

First, we need to convert the mixed numbers for the durations of the eclipses into improper fractions.

For the June 21 eclipse: \[ 3 \frac{2}{3} = 3 + \frac{2}{3} = \frac{9}{3} + \frac{2}{3} = \frac{11}{3} \]

For the March 29 eclipse: \[ 6 \frac{7}{15} = 6 + \frac{7}{15} = \frac{90}{15} + \frac{7}{15} = \frac{97}{15} \]

To subtract these fractions, we need a common denominator. The denominators are 3 and 15. The least common multiple of 3 and 15 is 15.

Convert \(\frac{11}{3}\) to a fraction with a denominator of 15: \[ \frac{11}{3} = \frac{11 \times 5}{3 \times 5} = \frac{55}{15} \]

Now, subtract the duration of the June 21 eclipse from the duration of the March 29 eclipse: \[ \frac{97}{15} - \frac{55}{15} = \frac{97 - 55}{15} = \frac{42}{15} \]

Simplify \(\frac{42}{15}\) by finding the greatest common divisor (GCD) of 42 and 15, which is 3: \[ \frac{42}{15} = \frac{42 \div 3}{15 \div 3} = \frac{14}{5} \]

Convert \(\frac{14}{5}\) to a mixed number: \[ \frac{14}{5} = 2 \frac{4}{5} \]

Final Answer