To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{6 x 5}{6 x 5} \) + \( \frac{7 x 3}{10 x 3} \)

\( \frac{30}{30} \) + \( \frac{21}{30} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{30 + 21}{30} \) = \( \frac{51}{30} \) = 1\(\frac{7}{10}\)

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 6 workers at the company now and that's enough to staff 2 crews so there are \( \frac{6}{2} \) = 3 workers on a crew. 4 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 4 x 3 = 12 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 12 - 6 = 6 new staff for the busy season.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{11 + 7 + 11 + 7}{4} \) = \( \frac{36}{4} \) = 9

50% of the water consumption is industrial use and 15% is personal use so (50% - 15%) = 35% more water is used for industrial purposes. 25,000 gallons are consumed daily so industry consumes \( \frac{35}{100} \) x 25,000 gallons = 8,750 gallons.

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.