Afreight train completes its journey of 150 miles 1 hour earlier if it’s original speed is increased by 5 miles/hour. what is the trains original speed?

Let s represent the train's original speed.

time = distance / speed

150/s = 150/(s +5) +1 . . . . . . . the original journey took 1 hour longer than at the faster speed

Multiply by s(s+5).
  150(s +5) = 150s +s(s+5)
  s^2 +5s -750 = 0 . . . . . . . rearrange to standard form
  (s +30)(s -25) = 0 . . . . . . . factor
Solutions to this are values of s that make the factors zero.
  s = -30 or +25 . . . . . . . . . only the positive solution makes sense

The train's original speed is 25 mph.