I tried everything and cannot get this answer, its my last problem. Can someone help? Possibly explain it along the way step by step?
One morning, for her Mile Club Challenge, Colleen ran 4 miles. When she got tired, she walked 7 miles. Colleen runs 4 mph faster than she walks. If she logged 1.1 hours that day in running/walking, find her walking speed and her running speed.
ranjankar
Let speed of walking be x mph
Speed of running =x+4 mph
4/ (x+4) + 7/x = 1.1
4x + 7(x+4) = 1.1x ( x+4)
4x +7x +28 = 1.1x^2 + 4.4x
1.1x^2 - 6.6x - 28 = 0
DIVIDE BY 1.1
x^2 - 6x - 25.45= 0
x^2 -6x = 25.45
ADD 9
x^2 -6x +9 = 34.45
( x - 3)^2= 34.45
x = 3 + \/34.45 = 8.87 mph
ANSWER 8.87 mph ( walking speed ) AND 12.87 mph ( running speed )
CHECK
4 /12.87 = 0.31 hours
7/8.87 = 0.79 hours
ADD = 1.1 hours
Mike G
w = walking speed
7/w + 4/(w+4) = 1.1
7w+28+4w = 1.1w^2+4.4w
1.1w^2-6.6w-28
Use the quadratic formula
w = 8.87
walking = 8.87 km/h
running = 12,87 km/h
Battleaxe
4mi/(x mi/h) + 7mi/(x - 4mi/hr) = 1.1hr
4/x + 7/(x - 4) = 1.1
common denominators:
4(x - 4)/x(x - 4) + 7x/x(x - 4) = 1.1x(x - 4)/x(x - 4)
4(x - 4) + 7x = 1.1x(x - 4)
4x - 16 + 7x = 1.1x^2 - 4.4x
1.1x^2 - 15.4x + 16 = 0
using quadratic formula:
x = [15.4 +/- SQR(237.16 - 4(1.1)(16))]/2(1.1)
x = [15.4 +/- SQR(166.76)]/2.2
x = [15.4 +/- 12.9]/2.2
x = 14.2, 1.25
14.2 mi/hr is the relevant root (running speed)
Walking speed is 4mi/hr less, so 14.2 - 4 = 10.2mi/hr
Running speed 14.2mi/hr, walking speed 10.2mi/hr.
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