SOLUTION: Can you help with this word problem please? Rachel allows herself 1 hour to reach a sales appointment 50 miles away. After she has driven 30 miles, she realizes that she must i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you help with this word problem please? Rachel allows herself 1 hour to reach a sales appointment 50 miles away. After she has driven 30 miles, she realizes that she must i      Log On


   

Question 239035: Can you help with this word problem please?
Rachel allows herself 1 hour to reach a sales appointment 50 miles away. After she has driven 30 miles, she realizes that she must increase her speed by 15mph in order to get there on time. What was her speed for the first 30 miles?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Rachel allows herself 1 hour to reach a sales appointment 50 miles away. After she has driven 30 miles, she realizes that she must increase her speed by 15mph in order to get there on time. What was her speed for the first 30 miles?
-------------------------------
1st leg DATA:
distance = 30 miles ; rate = x mph ; time = d/r = 30/x hrs
==========================
2nd leg DATA:
distance = 20 miles ; rate = x+15 mph ; time = d/r = 20/(x+15) hrs.
-------------------------
Equation:
time + time = 1 hr
30/x + 20/(x+15) = 1
30(x+15) + 20x = x(x+15)
x^2 +15x = 50x + 450 = 0
x^2 - 35x - 450 = 0
x = 45 mph (her rate for the first 30 miles)
===============================================
Cheers,
Stan H.