It took Eric 11 hours to drive to a football game. On the way home, he was able to increase his average speed by 12mph and make the return drive in only 9 hours. Find his average speed on the return drive.

54mph

Explanation:

Speed is defined as the change in distance of a body with respect to time.

Let x be the speed of Eric on his way to the football game, if he used 11hours to the football game, his distance will be the product of his speed and time taken i.e

Distance = speed × time

Distance= x × 11

Distance = 11x... (1)

During his return journey, his speed increases by 12mph with a return drive in only 9hours i.e speed = x+12 and time is 9hours

Since distance = speed × time (return Journey)

Distance = (x+12)×9

Distance = 9x+84...(2)

Note that the distance to and fro the journey is the same as such we will equate equations 1 and 2 to get his initial speed "x" to have;

11x = 9x+84

11x-9x = 84

2x = 84

x = 42mph

This means that his initial speed on his way to the football game is 42mph. Since his speed increases by 12mph during his return drive, his return speed will be 42mph + 12mph which gives 54mph.

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