-- We don't know the distance yet, but we have to call it something so that we can work with it.
I have chosen to represent the distance with the symbol ' D ' .
-- The time it took him to GO to the airport was D/90 hours.
-- The time it took him to RETURN from the airport was D/120 hours.
-- The total time for the round trip was (D/90 + D/120).
The Arithmetic:
Total 2-way time = (D/90) + (D/120)
Common denominator: (D/90) + (D/120) = 210D / 10,800
Total flying time given: 210D / 10,800 = 7 hours
Multiply each side by 10,800: 210D = 75,600
Divide each side by 210: D = 360 miles
Check:
Going . . . 360 miles / 90 mph = 4 hours
Returning . . . 360 miles / 120 mph = 3 hours
Total time . . . 4 hrs + 3 hrs = 7 hrs yay!
Note:
You can't just average the two numbers and call that his average speed for the round trip.
-- Average of 90 mph and 120 mph is (1/2)(90+120) = 105 mph
-- His actual average speed was (720mi/7hr) = 102.86 mph
