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

Algebra ->  Expressions -> 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      Log On


   

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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = her walking speed
+12s+ = her running speed
Let +t+ = her time spent walking
+7+-+t+ = her time spent running
-----------------------------------------
(1) +30+=+s%2At+
(2) +1+=+12s%2A%28+7+-+t+%29+
------------------------------
(1) +t+=+30%2Fs+
(2) +1+=+12s%2A%28+7+-+30%2Fs+%29+
(2) +1+=+84s+-+360+
(2) +84s+=+361+
(2) +s+=+4.298+ mi/hr
and
+12s+=+51.57+ mi/hr
------------------------------
check:
(1) +t+=+30%2Fs+
(1) +t+=+30%2F4.298+
(1) +t+=+6.981+ hrs
and
(2) +1+=+12s%2A%28+7+-+t+%29+
(2) +1+=+12%2A4.298%2A.019+
(2) +1+=+.9799+
close enough -check the math



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

RUN            r           30%2Fr             30

WALK          r%2F12        1%2F%28r%2F12%29               1

TOTAL                        7

highlight_green%2830%2Fr%2B12%2Fr=7%29
-
42%2Fr=7

6%2Fr=1

highlight%28r=6%29

Answer by MathTherapy(10555) About Me  (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 = matrix%281%2C4%2C+7%2F14%2C+or%2C+1%2F2%2C+mph%29 

Running speed: highlight_green%28matrix%281%2C4%2C+12+%2A+%281%2F2%29%2C+%22=%22%2C+6%2C+mph%29%29