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

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)\(4\leq{x}\leq{16}\)

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?

Yes, perfectly clear now. The bolded and underlined parts were what I was missing. Thank you!

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

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.

Answer: D

Home to school: 10

School to football: 4

Football to friend's house: 2

Case I: Home -----------------> School -----------------> Football -------------------> friend's house

He goes from Home to School then football practice and then friend's house and this are in one direction.

=> 10 + 4 + 2 = 16

Case II: Home -----------------Friend's house <-----------------Football <------------------- School

He goes from Home to school and while returning back goes for football practice and then goes to a friend's house in the same direction.

=> 10 - 4 - 2 = 4

Possible ranges for 'x': 4 ≤ x ≤ 16

Answer D

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