On saturday, the gomez family left home to a resort in maine. the drove at an average rate of 48 mph. on thursday they went back home traveling at an average speed of 40 mph because of work construction. if the gomez family spent 11 hours driving to and from the resort in maine, how many miles did they travel from their house to the resort? show work

If we set the unknown distance (in miles) as x, then we set up an equation according to the data, we can solve for x.

Time taken to go to resort : x/48
Time taken to return : x/40
Total time = x/48+x/40 = 11
Solve for x
common multiple between 48 and 40 = 240
so 
5x/240 + 6x/240 = 11
(5x+6x)/240 = 11
11x  = 11*240, => x=240
Distance from home to resort is 240 miles