Question

Amir went on a bike ride of 60 miles. He realized that if he had gone 5 mph faster, he would have arrived 6 hours sooner. How fast did he actually ride? Amir rode mph on his trip.

Answer 1

Explanation:

distance / rate = time

x = original speed mph

60/x = t

Then at 5 mph faster

60/(5+x) = t - 6 re-arranged for t = 60/(5+x) + 6

equate the two definitions of 't' then solve for 'x'

60/x = 60/(5+x) + 6

60 = 60x/(5+x) + 6x

60(5+x) = 60x +6x(5+x)

300 + 60x = 60x + 30x + 6x^2

6x^2 +30x -300 = 0 Use Quadratic Formula to find x = 5 m/hr