<PRE><B>Question 530172</B>
a train travels 180 miles in an hour less time than a bus traveling the same distance.
 if the speed of the bus is 15 mph slower that the speed of the train, find the speed of the train and bus? 
:
Let s = speed of the bus
then
(s+15) = speed of the train
:
Write a time equation, time = dist/speed
:
Bus time - train time = 1 hr
{{{180/s}}} - {{{180/(s+15)}}} = 1
;
multiply by s(s+15); results:
180(s+15) - 180s = s(s+15)
180s + 2700 - 180s = s^2 + 15s
:
a quadratic equation
s^2 + 15s - 2700 = 0
:
Factor to
(s+60)(s-45) = 0
:
the positive solution
s = 45 mph is the speed of the bus
then
45 + 15 = 60 mph is the speed of the train
:
:
Check this by finding the times of each
180/45 = 4 hrs
180/60 = 3 hrs
--------------
differ:  1 hrs</PRE>