Kiran drove from Tortula to catctus a distance of 280mi. She increased her speed by 15mi/h for the 384 mi trip from cactus to dry Junction. If the totsl trip took 8 hours,what was her speed from tortula to cactus?

Let s represent Kiran's speed from Tortula to Cactus. The trip time can be written as
  280/s + 384/(s+15) = 8
  280(s+15) + 384(s) = 8(s)(s+15)    (multiply by s(s+15))
  0 = 8s^2 - 544s - 4200    (subtract the left side)
  0 = s^2 - 68s - 525    (divide by 8)
  1681 = (s-34)^2    (add 525+34^2)
  34 ± 41 = s    (square root and add 34)
  s = -7, 75

Kiran drove from Tortula to Cactus at 75 mph.