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# Bills' school is 10 miles from his home. He travels 4 miles from schoo

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Bills' school is 10 miles from his home. He travels 4 miles from schoo  [#permalink]

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19 Jun 2016, 03:48
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Bills' school is 10 miles from his home. He travels 4 miles from school to football practice, and then 2 miles to friend's house. If he is then x miles from home, what is the range of possible values for x?

a) $$2\leq{x}\leq{10}$$

b) $$4\leq{x}\leq{10}$$

c) $$4\leq{x}\leq{12}$$

d)$$4\leq{x}\leq{16}$$

e) $$6\leq{x}\leq{16}$$

At most 16 and at least 4
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Re: Bills' school is 10 miles from his home. He travels 4 miles from schoo  [#permalink]

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19 Jun 2016, 05:07
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bimalr9 wrote:
Bills' school is 10 miles from his home. He travels 4 miles from school to football practice, and then 2 miles to friend's house. If he is then x miles from home, what is the range of possible values for x?

a) $$2\leq{x}\leq{10}$$

b) $$4\leq{x}\leq{10}$$

c) $$4\leq{x}\leq{12}$$

d)$$4\leq{x}\leq{16}$$

e) $$6\leq{x}\leq{16}$$

At most 16 and at least 4

1.If his football ground and his friend's house lie on the way to his house.
then the distance can be minimum .
10 -(4+2) = 4

2.If his football ground and his friends house lie in the opposite direction from the way to his house.
this will then give us the maximum distance.
10+(4+2) = 16

therefore , x will lie between 4 and 16
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Re: Bills' school is 10 miles from his home. He travels 4 miles from schoo  [#permalink]

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19 Jun 2016, 05:10
bimalr9 wrote:
Bills' school is 10 miles from his home. He travels 4 miles from school to football practice, and then 2 miles to friend's house. If he is then x miles from home, what is the range of possible values for x?

a) $$2\leq{x}\leq{10}$$

b) $$4\leq{x}\leq{10}$$

c) $$4\leq{x}\leq{12}$$

d)$$4\leq{x}\leq{16}$$

e) $$6\leq{x}\leq{16}$$

At most 16 and at least 4

Case - I

Home -----10------School----4------Football---2----Friend ( Total distance is 10+4+2 = 16)

Case - II

Home ----------------------10-------------------------------School

Home -------4------Friend-------2-------Football-----4---School ( He is 4 meters away from home )

So, Correct answer will d)$$4\leq{x}\leq{16}$$
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Bills' school is 10 miles from his home. He travels 4 miles from schoo  [#permalink]

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26 Jun 2017, 08:31
bimalr9 wrote:
Bills' school is 10 miles from his home. He travels 4 miles from school to football practice, and then 2 miles to friend's house. If he is then x miles from home, what is the range of possible values for x?

a) $$2\leq{x}\leq{10}$$

b) $$4\leq{x}\leq{10}$$

c) $$4\leq{x}\leq{12}$$

d)$$4\leq{x}\leq{16}$$

e) $$6\leq{x}\leq{16}$$

At most 16 and at least 4

bimalr9, Bunuel, or anyone, how do we assume that the options for travel are on the same line of travel as home to school?

Maybe I'm missing something, but I think this question is confusing because it doesn't indicate that the places he visits are either beyond the school on the same line of travel, or between school and home.

It wasn't self-evident, and I had to run the numbers to make sure my Case III below was not a possibility.

There seems to be a Case III: suppose the school is due east of Bill's house. Suppose football practice is due south (or north) of the school. Suppose the friend's house is due south (or north) of the school and football practice.

Then one of the possibilities for "x miles from home" is then the hypotenuse of a right triangle.

What am I missing?
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Bills' school is 10 miles from his home. He travels 4 miles from schoo  [#permalink]

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26 Jun 2017, 09:04
1
genxer123 wrote:
bimalr9 wrote:
Bills' school is 10 miles from his home. He travels 4 miles from school to football practice, and then 2 miles to friend's house. If he is then x miles from home, what is the range of possible values for x?

a) $$2\leq{x}\leq{10}$$

b) $$4\leq{x}\leq{10}$$

c) $$4\leq{x}\leq{12}$$

d) $$4\leq{x}\leq{16}$$

e) $$6\leq{x}\leq{16}$$

At most 16 and at least 4

bimalr9, Bunuel, or anyone, how do we assume that the options for travel are on the same line of travel as home to school?

Maybe I'm missing something, but I think this question is confusing because it doesn't indicate that the places he visits are either beyond the school on the same line of travel, or between school and home.

It wasn't self-evident, and I had to run the numbers to make sure my Case III below was not a possibility.

There seems to be a Case III: suppose the school is due east of Bill's house. Suppose football practice is due south (or north) of the school. Suppose the friend's house is due south (or north) of the school and football practice.

Then one of the possibilities for "x miles from home" is then the hypotenuse of a right triangle.

What am I missing?

We are interested in the range of x. The range would be the difference between the greatest value of x and the smallest value of x. Both will occur if all 4 destionations are on a straight line.

The greatest value:

H----------S----FB--F

10 + 4 + 2 = 16.

The smallest value:

H----F--FB----S

10 - 4 - 2 = 4

Range: $$4\leq{x}\leq{16}$$

Hope it's clear.
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Bills' school is 10 miles from his home. He travels 4 miles from schoo  [#permalink]

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26 Jun 2017, 09:16
Bunuel wrote:

We are interested in the range of x. The range would be the difference between the greatest value of x and the smallest value of x. Both will occur if all 4 destionations are on a straight line.

Hope it's clear.

Yes, perfectly clear now. The bolded and underlined parts were what I was missing. Thank you!
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Re: Bills' school is 10 miles from his home. He travels 4 miles from schoo  [#permalink]

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26 Jun 2017, 13:00
Bills' school is 10 miles from his home. He travels 4 miles from school to football practice, and then 2 miles to friend's house. If he is then x miles from home, what is the range of possible values for x?

Bills House ============ School ==== Football Practice ==Friend's House
======================10======================4=======================2

As per the above Figure

Maximum distance will be if Bill travels exactly in straight line for all these stops

Maximum Distance $$= 10 + 4 + 2 = 16$$

Minimum distance will be if Bill travels exactly opposite and in straight line of his way to school

Minimum Distance $$= 10 - 4 - 2 = 4$$

Hence, the range can be defined by:

$$4\leq{x}\leq{16}$$

Hence, Answer is D
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Re: Bills' school is 10 miles from his home. He travels 4 miles from schoo  [#permalink]

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28 Jun 2017, 16:54
bimalr9 wrote:
Bills' school is 10 miles from his home. He travels 4 miles from school to football practice, and then 2 miles to friend's house. If he is then x miles from home, what is the range of possible values for x?

a) $$2\leq{x}\leq{10}$$

b) $$4\leq{x}\leq{10}$$

c) $$4\leq{x}\leq{12}$$

d)$$4\leq{x}\leq{16}$$

e) $$6\leq{x}\leq{16}$$

When Bill is at school, he is 10 miles from home. Since Bill travels 6 miles from school for his two activities, he could be as close as x = 10 - 6 = 4 miles from home or as far as 10 + 6 = 16 miles from home.

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Re: Bills' school is 10 miles from his home. He travels 4 miles from schoo  [#permalink]

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08 Jan 2019, 08:19
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Re: Bills' school is 10 miles from his home. He travels 4 miles from schoo   [#permalink] 08 Jan 2019, 08:19
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