SOLUTION: Rachel allows hersef 1 hr to reach a sales appointment 50 mi away. After she has driven 30 mi, she realizes that she must increase her speed by 15 mph in order to get there on tim

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Question 307801: Rachel allows hersef 1 hr to reach a sales appointment 50 mi away. After she has driven 30 mi, 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 mi?
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
Rachel allows hersef 1 hr to reach a sales appointment 50 mi away. After she has driven 30 mi, 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 mi?
Let her initial speed be x mph
time taken if she traveled that speed for 30 km = 30/x
she increased her speed to by 15 mph
her new speed = x+15 mph
time taken by driving with new speed = 20/x+15 hours
Actual time taken = 30/x + 20/ x+15 hours
30/x + 20/ x+15 =1
lcm = x(x+15)
30(x+15)+20x= x(x+15)
30x+450 +20x= x^2 +15x
x^2+15x-30x-20x-450 =0
x^2-35x-450=0
x^2 -45x+10x-450=0
x(x-45)+10(x-45)=0
(x+10)(x-45)=0
x=-10 OR x =45
-10 is not valid
So she drove at 45 mph for 30 miles