Let x be the rate of Twice the Prince (in ft/s);
then the rate of Secretariat is (x+1.7) ft/s.


The distance is the same for both runners, so we can write this equation for the distance

    144*(x+1.7) = 148.6x.


Simplify and find x

    144x + 144*1.7 = 148.6x

    244.8 = 148.6x - 144x

    244.8 = 4.6x

        x = 244.8/4.6 = 53.21739


Thus the rate of Twice the Prince is 53.21739 ft/s and the distance is 148.6*x= 148.6*53.21739 = 7908.1 feet.


ANSWER.  The distance is 7908 feet (rounded to nearest whole number of feet).

Secretariat completed the race in 144 seconds, and Twice a Prince finished in 148.6 seconds. How far was the race in feet if Secretariat ran about 1.7 feet per second faster than Twice a Prince? Round answer to the nearest whole number.

Let the distance, in feet, be D
Then Secretariat's speed = 
Also, Twice a Prince's speed = 
Since Secretariat's speed was 1.7 seconds faster than Twice a Prince's, we get the 
following SPEED equation: 
                     148.6D = 144D + 144(148.6)(1.7) ----- Multiplying by LCD, 144(148.6)
              148.6D - 144D = 144(148.6)(1.7)
                       4.6D = 144(148.6)(1.7)
Distance of race, or