The Fairfax County Water Authority has approved a 15 per cent increase in water rates, raising the average Fairfax customer's bill to $78.80 a year.

In addition, the fee charged builders to connect new homes to the water system in Fairfax will be raised from $1.125 to $2.000.

The nine-member independent authority, whose members are appointed by the Fairfax County board of supervisors, has the power to impose increased rates after a public hearing. The necessary hearing was held on June 25.

The rate increases, which will go into effect Aug. 1, are necessary to meet the rising cost of maintaining the present water system and the higher cost of borrowing money for construction, according to Jim Warfield, the authority spokesman.

Warfield said "inflationary factors" have made it impossible for the water authority to operate under its present revenues.

Warfield said the increases will bring in an estimated $71 million in additional revenue over the next 10 years. More than half - $41 million - is expected to come from the increase in connection fees.

David Miller, president of the Northern Virginia Builders Association, said the higher connection fee will add $475 to the price of a new single-family home because the cost will be passed onto the home buyer. The median price of a home in Fairfax is $64,600.

Water rates for customers in Alexandria and parts of Prince William County will also go up as a result of the Fairfax Water Authority increases. Both jurisdictions buy their water from Fairfax, but the exact amounts of the increases have not been announced.

Prince William County officials have bitterly opposed any increase in the water rates. they say the county is being overcharged for water.

Besides Fairfax, Prince William and Alexandria, the authority serves Ft. Belvoir and Lorton Reformatory - a total of 616.200 customers. The system's average customer uses 94,000 gallons a year. The average shower uses 20 gallons of water.

In 1974, the water authority increased its rates by 26 per cent. At that time, authority officials said that increase would take care of expenses for 10 years.

But last year, lawyers retained to advise the authority on selling bonds, told the authority it would have to impose another incrase - seven years ahead of schedule.

The rate increase was neccessary, the lawyers said, to assure enough revenue to pay off bonds sold in the future. The authority plans to sell $54 million in revenue bonds to finance expansion and improvements.

Under a trust agreement with purchasers of old bonds, the authority must have rates that will automatically cover all principal and interest payments on bonds already sold and those in plans to sell over the next year. The trust agreement also stipulates a 10 per cent margin of safety and even stiffer requirements once construction is finished.

The biggest item in the construction plan is the authority's proposed facility to take water from the Potomac River.