As part of his flight training, a student pilot was required to fly to an airport and then return. the average speed to the airport was 90 mph, and the average speed returning was 120 mph. find the distance between the two airports if the total flying time was 7 hours.

-- 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

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