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!

Time = Distance/Speed

Let d represent the distance from home to the resort in miles.
Time To Resort = d/48
Time To Home = d/40
Total Time = Time To Resort + Time To Home
11 = d/48 +d/40 . . . . . . . . . . substitute known values & expressions
.. = d*(40 +48)/(40*48) . . . . add fractions
.. = d*11/240 . . . . . . . . . . . . . simplify
11*(240/11) = d . . . . . . . . . . . multiply by the inverse of the coefficient of d
240 = d

The Gomez family traveled 240 miles from their house to the resort.