Nick went on a bike ride of 90 miles. he realized that if he had gone 12 mph faster, he would have arrived 10 hours sooner. how fast did he actually ride?

Answer 1

rt = d

Let Nick's rate be r

Then, as d = 90, t = 90/r

If he goes 12 mph faster, his rate will be r + 12.

90/(r+12) = 90/r - 10

90/(r+12) = (90 - 10r)/r

90r = 90r + 1080 - 10r^2 - 120r

1080 - 120r - 10r^2 = 0

r^2 + 12r - 108 = 0

(r+18)(r - 6) = 0

Clearly, the negative rate does not make sense.

Thus, r = 6

To check:

90/6 = 15

90/(6+12) = 90/18 = 5

15 - 5 = 10