SOLUTION: 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

Question 241089: 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?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 =
:
1st 30 mi time + last 20 mi time = 1 hour
+ = 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
+ =
+ = 1 hr

RELATED QUESTIONS
Rachel allows herself 1 hr to reach a sales appointment 50 miles away. After she has... (answered by jojo14344)

Rachel allows herself 1 hour to reach a sales appointment 50 miles away. After she has... (answered by ankor@dixie-net.com)

Rachel allows herself 1 hour to reach a sales appointment 50 miles away. After she has... (answered by nerdybill)

Can you help with this word problem please? Rachel allows herself 1 hour to reach a... (answered by stanbon)

Rachel allows herself 1 hr to reach a sales appointment 50 mi away. After she has driven (answered by stanbon)

1. Solve (3a-5)(a�+4a+3) + (2a+2)(a+3) = (a-3)(a+1) 2. Rachel allows herself 1... (answered by josmiceli)

Rachel allows hersef 1 hr to reach a sales appointment 50 mi away. After she has driven... (answered by mananth)

1. Solve (3a-5)/(a�+4a+3)+(2a+2)/(a+3)=(a-3)/(a+1) 2. Rachel allows herself 1... (answered by Alan3354)

rachel allows herself 1hr to reach a sales appointment 50mi away. After she has driven... (answered by stanbon)