The Price River is a 137-mile-long southeastward flowing river in Carbon, Utah and Emery counties in eastern Utah. It is a tributary to the Green River, itself a tributary to the Colorado River. The river's early name was the White River, but it was changed in the summer of 1869 when LDS Bishop William Price of Goshen, Utah, explored the region and rena…The Price River is a 137-mile-long southeastward flowing river in Carbon, Utah and Emery counties in eastern Utah. It is a tributary to the Green River, itself a tributary to the Colorado River. The river's early name was the White River, but it was changed in the summer of 1869 when LDS Bishop William Price of Goshen, Utah, explored the region and renamed it, making the White River above Colton into a tributary of the Price River. The town of Price was later named after the river.