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

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Question 271148: Rachel allows herself 1 hr to reach a sales appointment 50 mi away. After she has driven 30 mi, she realizes she must increase her speed by 15 mph in order to get there on time. What was her speed for the first 30 mi? I cannot familiarize this problem and it's driving me nuts. I am taking an online course and it's hard. I have tried to come up with a formula... If she travels x miles per hour for 30 miles and x+15 miles per hour for 20 miles she would get there in 60 mins, or one hour. x+x+15=50? wait miles per hour is distance/time. so 50 miles / 1hour. and she travels at x for 30 so 30 times x? I am so lost on this problem. I have tried a bunch more ways that don't make sense. Once i got x=1. She obviously did not travel at one mile per hour or she would never had made it 50 miles in one hour! It would be so much more funny if I wasn't dying over this problem!
Found 2 solutions by Greenfinch, mananth:
Answer by Greenfinch(383) About Me  (Show Source):
You can put this solution on YOUR website!
After 30 miles time is 30/x
Next part is 20/(x + 15)
So 30/x + 20/(x + 15) = 1
LCM is x(x+15
so 30(x + 15) + 20x = x(x+15)
30x + 450 + 20x = x^2 + 15x
x^2 - 35x - 450 = 0
(x - 45)(X + 10) = 0
x = 45 or -10
initial speed is 45 mph

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Rachel allows herself 1 hr to reach a sales appointment 50 mi away. After she has driven 30 mi, she realizes she must increase her speed by 15 mph in order to get there on time. What was her speed for the first 30 mi?
FIRST HALF HOUR
let the speed she travelled for the first half hour be x mph
distance traveled in the first half hour will be 1/2 * x MILES
SECOND HALF HOUR
SPEED FOR THE NEXT HALF HOUR WAS X+15 MPH
DISTANCE TRAVELLED WILL BE (X+15) *1/2 miles
the total distance she traveled was 50 miles
1/2*x + 1/2*(x+15) =50
x+x+15 = 2*50
2x= 100-15
x=85/2 = 42.5 mph. In the second half hour it will be 42.5 +15 = 57.50 mph
Confirmation :
First half hour she travels 21.25 miles. In the second half hour she travels 28.75 miles.
the sum of these two is 50 miles.
Hope it is clear
Have fun with Math