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r-ruslan [8.4K]
3 years ago
6

RSM QUESTION NEED HELP!!!!!! A biker traveling at his usual speed can go from his house to work in 4 hours. When the weather is

bad, he travels 6 miles per hour slower, and it takes him half an hour more. How far is his work from his house?
Mathematics
1 answer:
kogti [31]3 years ago
3 0
<h3>Answer:   216 miles</h3>

=======================================

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

------------------------

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

----------------------

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

----------------------

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.

----------------------

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.

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So, probability that the sample proportion (the proportion living in the dormitories) is between 0.70 and 0.85 is given by = P(0.70 < \hat p < 0.85)

     P(0.70 < \hat p < 0.85) = P( \hat p < 0.85) - P( \hat p \leq 0.70)

     P( \hat p < 0.85) = P( \frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < \frac{0.85-0.80}{\sqrt{\frac{0.85(1-0.85)}{80} } } ) = P(Z < 1.25) = 0.89435

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<em />

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