<PRE><B>Question 688467</B>
When the speed of a train is increased by 10 mph, it can cover a 300 mile route in one hour less time.
 What is the original speed of the train?
:
Let s = the original speed of the train
:
Write a time equation, time = dist/speed
:
Original time - faster time = 1 hr
{{{300/s}}} - {{{300/((s+10))}}} = 1
Multiply by s(s+10), this clears the denominators, resulting in:
300(s+10) - 300s = s(s+10)
:
300s + 3000 - 300s = s^2 + 10s
A quadratic equation
0 = s^2 + 10s - 3000 
This factors to
(s+60(s-50) = 0
the positive solution is what we want here
s = 50 mph is the original speed
:
:
Confirm this find the time of each scenario
300/50 = 6 hrs
300/60 = 5 hrs, 1 hr less</PRE>