<PRE><B>Question 241089</B>
Rachel allows herself 1 hr to reach a sales appointment 50 miles away.
 After she has driven 30 miles, she realizes that she must increase her speed by 15 mph in order to get there on time.
What was her speed for the first 30 miles? 
:
Let s = speed for the 1st 30 mi
then
(s+15) = speed for the last 20 miles
:
Write a time equation: Time = {{{dist/speed}}}
:
1st 30 mi time + last 20 mi time = 1 hour
{{{30/s}}} + {{{20/((s+15))}}} = 1
Multiply equation by s(s+15), results
30(s+15) + 20s = s(s+15)
:
30s + 450 + 20s = s^2 + 15s
:
50s + 450 = s^2 + 15s
Arrange as a quadratic equation
0 = s^2 + 15s - 50s - 450
:
s^2 - 35s - 450 = 0
Factor 
(s - 45)(s + 10) = 0
positive solution
s = 45 mph for the 1st 30 mi
then
45 + 15 = 60 mph for the last 20 mi
;
:
See if that adds up
{{{30/45}}} + {{{20/60}}} =
{{{2/3}}} + {{{1/3}}} = 1 hr
 </PRE>