SOLUTION: To prepare for a marathon​ run, Sue ran 30 miles before she blistered her​ heel, and then she walked 1 additional mile. Her running speed was 12 times as fast as her walking sp

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Question 1142664: To prepare for a marathon​ run, Sue ran 30 miles before she blistered her​ heel, and then she walked 1 additional mile. Her running speed was 12 times as fast as her walking speed. She was running and walking for 7 hours. Find​ Sue's running speed.
Found 4 solutions by Alan3354, josmiceli, josgarithmetic, MathTherapy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
To prepare for a marathon​ run, Sue ran 30 miles before she blistered her​ heel, and then she walked 1 additional mile. Her running speed was 12 times as fast as her walking speed. She was running and walking for 7 hours. Find​ Sue's running speed.
-------
r = run speed
w = walk speed
-------
30/r + 1/w = 7
r = 12w
-----
30/12w + 1/w = 7
30/12 + 1 = 7w
7w = 3.5
w = 0.5 mi/hr
r = 6 mi/hr
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = her walking speed
= her running speed
Let = her time spent walking
= her time spent running
-----------------------------------------
(1)
(2)
------------------------------
(1)
(2)
(2)
(2)
(2) mi/hr
and
mi/hr
------------------------------
check:
(1)
(1)
(1) hrs
and
(2)
(2)
(2)
close enough -check the math



Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
               SPEED        TIME       DISTANCE

RUN            r                        30

WALK                                 1

TOTAL                        7


-





Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
To prepare for a marathon​ run, Sue ran 30 miles before she blistered her​ heel, and then she walked 1 additional mile. Her running speed was 12 times as fast as her walking speed. She was running and walking for 7 hours. Find​ Sue's running speed.
This is NOT NEARLY as complex as @josmiceli makes it. Plus, his walking speed of 4.298 is WRONG



It's a little more "INVOLVED" if I use S as the running speed, so I'll use S as the walking speed

Then running speed = 12S

We then get: 

5 + 2 = 14S ------ Multiplying by LCD, 2S

7 = 14S

S, or walking speed =  

Running speed:  

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