Answer: 216 miles
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Work Shown:
d = distance from work to his house
x = speed when weather is good
y = speed when weather is bad
y = x-6 since he travels 6 mph slower
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On a good weather day, he travels for 4 hours and goes at x mph
distance = rate*time
d = r*t
d = x*4
d = 4x
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On a bad weather day, he travels 4.5 hours (half hour more than 4 hrs) and goes at y = x-6 mph
d = r*t
d = y*4.5
d = 4.5y
d = 4.5(x-6) .... replace y with x-6
d = 4.5x-27 .... distribute
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The values of d for both equations are the same, as the biker is traveling the same distance. So we can equate the two right hand sides (RHS) and solve for x.
4.5x-27 = 4x
4.5x-4x = 27
0.5x = 27
x = 27/0.5
x = 54
The biker's speed on a good weather day is 54 mph.
A bad weather day's speed would be y = x-6 = 54 - 6 = 48 mph.
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Now compute the value of d
d = 4x
d = 4*54
d = 216
The biker travels 216 miles on a good weather day
or,
d = 4.5*y
d = 4.5*48
d = 216
the biker travels that same distance on a bad weather day.
