SOLUTION: Bill runs 5 miles then walks 1 mile. He runs 6 mph faster than he walks. If his total time yesterday was 45 minutes. how fast did he run? I tried many different things: I kno

Question 360591: Bill runs 5 miles then walks 1 mile. He runs 6 mph faster than he walks. If his total time yesterday was 45 minutes. how fast did he run?
I tried many different things: I know I need to use d=rt somehow. I believe his run rate is 5/x+6 and his walk rate is 1/x. I have tried 5/x+6 + 1/x = 6 and also setting it equal to 45, but not getting the correct answer (x=4).
Thanks in advance for your assistance.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Bill runs 5 miles then walks 1 mile. He runs 6 mph faster than he walks. If his total time yesterday was 45 minutes. how fast did he run?
----
Walk DATA:
distance = 1 mile ; rate = x mph ; time = 1/x hrs
---------
Run DATA:
distance = 5 miles; rate = x+6 mph ; time = 5/(x+6) hrs
------------------
Equation:
time + time = 3/4 hr
---
1/x + 5/(x+6) = 3/4 hr
----
Multiply thru by 4x(x+6):
4(x+6) + 5(4x) = 3x(x+6)
----
4x+24 + 20x = 3x^2+18x
---
3x^2 - 6x -24 = 0
x^2 - 2x - 8 = 0
(x-4)(x+2) = 0
Positive solution:
x = 4 mph (walking rate)
x+6 = 10 mph (running rate)
===============================
Cheers,
Stan H.
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